Dynamic correlations: exact and approximate methods for mutual information.

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.

Synergy and anti-cooperativity in allostery: Molecular dynamics study of WT and oncogenic KRAS-RGL1.

This study focuses on investigating the effects of an oncogenic mutation (G12V) on the stability and interactions within the KRAS-RGL1 protein complex. The KRAS-RGL1 complex is of particular interest due to its relevance to KRAS-associated cancers and the potential for developing targeted drugs against the KRAS system. The stability of the complex and the allosteric effects of specific residues are examined to understand their roles as modulators of complex stability and function. Using molecular dynamics simulations, we calculate the mutual information, MI, between two neighboring residues at the interface of the KRAS-RGL1 complex, and employ the concept of interaction information, II, to measure the contribution of a third residue to the interaction between interface residue pairs. Negative II indicates synergy, where the presence of the third residue strengthens the interaction, while positive II suggests anti-cooperativity. Our findings reveal that MI serves as a dominant factor in determining the results, with the G12V mutation increasing the MI between interface residues, indicating enhanced correlations due to the formation of a more compact structure in the complex. Interestingly, although II plays a role in understanding three-body interactions and the impact of distant residues, it is not significant enough to outweigh the influence of MI in determining the overall stability of the complex. Nevertheless, II may nonetheless be a relevant factor to consider in future drug design efforts. This study provides valuable insights into the mechanisms of complex stability and function, highlighting the significance of three-body interactions and the impact of distant residues on the binding stability of the complex. Additionally, our findings demonstrate that constraining the fluctuations of a third residue consistently increases the stability of the G12V variant, making it challenging to weaken complex formation of the mutated species through allosteric manipulation. The novel perspective offered by this approach on protein dynamics, function, and allostery has potential implications for understanding and targeting other protein complexes involved in vital cellular processes. The results contribute to our understanding of the effects of oncogenic mutations on protein-protein interactions and provide a foundation for future therapeutic interventions in the context of KRAS-associated cancers and beyond.

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.

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.

Fine tuning rigid body docking results using the Dreiding force field: A computational study of 36 known nanobody-protein complexes.

This paper aims to understand the binding strategies of a nanobody-protein pair by studying known complexes. Rigid body protein-ligand docking programs produce several complexes, called decoys, which are good candidates with high scores of shape complementarity, electrostatic interactions, desolvation, buried surface area, and Lennard-Jones potentials. However, the decoy that corresponds to the native structure is not known. We studied 36 nanobody-protein complexes from the single domain antibody database, sd-Ab DB, http://www.sdab-db.ca/. For each structure, a large number of decoys are generated using the Fast Fourier Transform algorithm of the software ZDOCK. The decoys were ranked according to their target protein-nanobody interaction energies, calculated by using the Dreiding Force Field, with rank 1 having the lowest interaction energy. Out of 36 protein data bank (PDB) structures, 25 true structures were predicted as rank 1. Eleven of the remaining structures required Ångstrom size rigid body translations of the nanobody relative to the protein to match the given PDB structure. After the translation, the Dreiding interaction (DI) energies of all complexes decreased and became rank 1. In one case, rigid body rotations as well as translations of the nanobody were required for matching the crystal structure. We used a Monte Carlo algorithm that randomly translates and rotates the nanobody of a decoy and calculates the DI energy. Results show that rigid body translations and the DI energy are sufficient for determining the correct binding location and pose of ZDOCK created decoys. A survey of the sd-Ab DB showed that each nanobody makes at least one salt bridge with its partner protein, indicating that salt bridge formation is an essential strategy in nanobody-protein recognition. Based on the analysis of the 36 crystal structures and evidence from existing literature, we propose a set of principles that could be used in the design of nanobodies.

Prediction of allosteric communication pathways in proteins.

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.

5-Fluoro/(trifluoromethoxy)-2-indolinone derivatives with anti-interleukin-1 activity.

The pro-inflammatory cytokine interleukin-1 (IL-1) drives the pathogenesis of several inflammatory diseases. Recent studies have revealed that 2-indolinones can modulate cytokine responses. Therefore, we screened several 2-indolinone derivatives in preliminary studies to develop agents with anti-IL-1 activity. First, the putative efficacies and binding interactions of 2-indolinones were evaluated by docking studies. Second, previously synthesized 5-fluoro/(trifluoromethoxy)-1H-indole-2,3-dione 3-(4-phenylthiosemicarbazones) (compounds 47-69) which had the highest inhibitory effect in the screening were evaluated for inhibitory effects on the IL-1 receptor (IL-1R). Compounds 52 (IC50 = 0.09 µM) and 65 (IC50 = 0.07 µM) were selected as lead compounds for the subsequent synthesis of new derivatives. The novel 5-fluoro/(trifluoromethoxy)-1H-indole-2,3-dione 3-(4-phenylthiosemicarbazones) (compounds 70-116) were designed, synthesized, and in vitro studies were completed. The compounds 76, 78, 81, 91, 100, 105, and 107 tested showed nontoxic inhibitory effects on IL-1R-dependent responses in the range of 0.01-0.06 µM and stronger than the lead compounds 52 and 65. In vitro and in silico findings showed that compounds 78 (IC50 = 0.01 µM) and 81 (IC50 = 0.02 µM) had the strongest IL-1R inhibitory effects and the most favorable drug-like properties. Molecular modeling studies of the compounds 78 and 81 were carried out to determine the possible binding interactions at the active site of the IL-1R.

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 modeled 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 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 givesB-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.

Information flow and allosteric communication in proteins.

Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer between residue pairs in proteins is developed. The joint distribution function for residue fluctuations required by the theory is expressed in terms of tensor Hermite polynomials that 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. The amount and speed of information transfer between residues, which are important for understanding allosteric activity in proteins, are discussed. Mutual information between two residues is commonly used for information transfer. 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. Peak values of calculated information transfer, ∼0.01-0.04 bits, are about two orders of magnitude smaller than the information content of residues. They are comparable to mutual information values, however. Estimated transfer rates are in the order of 1-20 megabits per second, and sustained transfer during the activity time-span of proteins may be significant. Information transfer from third order contributions is one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.

Binding Mechanism of Neutralizing Nanobodies Targeting SARS-CoV-2 Spike Glycoprotein.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) enters human cells upon binding of its spike (S) glycoproteins to ACE2 receptors. Several nanobodies neutralize SARS-CoV-2 infection by binding to the receptor-binding domain (RBD) of the S protein, but how their binding antagonizes S-ACE2 interactions is not well understood. Here, we identified interactions between the RBD and nanobodies H11-H4, H11-D4, and Ty1 by performing all-atom molecular dynamics simulations. H11-H4 and H11-D4 can bind to RBD without overlapping with ACE2. H11-H4, and to a lesser extent H11-D4, binding dislocates ACE2 from its binding site due to electrostatic repulsion. In comparison, Ty1 overlaps with ACE2 on RBD and has a similar binding strength to ACE2. Mutations in the Alpha variant of SARS-CoV-2 had a minor effect in RBD binding strengths of ACE2 and nanobodies, but reduced the ability of H11-H4 and H11-D4 to dislocate ACE2 from RBD. In comparison, the Beta variant weakened the RBD binding strengths of H11-H4 and H11-D4, which were less effective to dislocate ACE2 binding. Unexpectedly, mutations in Beta strengthened Ty1 binding to RBD, suggesting that this nanobody may be more effective to neutralize the Beta variant of SARS-CoV-2.

ModiBodies: A computational method for modifying nanobodies in nanobody-antigen complexes to improve binding affinity and specificity.

Nanobodies are special derivatives of antibodies, which consist of single domain fragments. They have become of considerable interest as next-generation biotechnological tools for antigen recognition. They can be easily engineered due to their high stability and compact size. Nanobodies have three complementarity-determining regions, CDRs, which are enlarged to provide a similar binding surface to that of human immunoglobulins. Here, we propose a benchmark testing algorithm that uses 3D structures of already existing protein-nanobody complexes as initial structures followed by successive mutations on the CDR domains. The aim is to find optimum binding amino acids for hypervariable residues of CDRs. We use molecular dynamics simulations to compare the binding energies of the resulting complexes with that of the known complex and accept those that are improved by mutations. We use the MDM4-VH9 complex, (PDB id 2VYR), fructose-bisphosphate aldolase from Trypanosoma congolense (PDB id 5O0W) and human lysozyme (PDB id 4I0C) as benchmark complexes. By using this algorithm, better binding nanobodies can be generated in a short amount of time. We suggest that this method can complement existing immune and synthetic library-based methods, without a need for extensive experimentation or large libraries.

A computational model for controlling conformational cooperativity and function in proteins.

We present a computational model that allows for rapid prediction of correlations among a set of residue pairs when the fluctuations of another set of residues are perturbed. The simple theory presented here is based on the knowledge of the fluctuation covariance matrix only. In this sense, the theory is model independent and therefore universal. Perturbation of any set of fluctuations and the resulting response of the remaining set are calculated using conditional probabilities of a multivariate normal distribution. The model is expected to rapidly and accurately map the consequences of mutations in proteins, as well as allosteric activity and ligand binding. Knowledge of triple correlations of fluctuations of residues i, j, and k, 〈 Δ R i Δ R j Δ R k 〉 emerges as the necessary source of information for controlling residue pairs by perturbing a distant residue. Triple correlations have not received wide attention in literature. Perturbation-response-function relations for ubiquitin (UBQ) are discussed as an example. Covariance matrix for UBQ obtained from the Gaussian Network Model combined with the present computational algorithm is able to reflect the millisecond molecular dynamics correlations and observed NMR results. © 2018 Wiley Periodicals, Inc.

Binding stability of peptides on major histocompatibility complex class I proteins: role of entropy and dynamics.

Prediction of peptide binding on specific human leukocyte antigens (HLA) has long been studied with successful results. We herein describe the effects of entropy and dynamics by investigating the binding stabilities of 10 nanopeptides on various HLA Class I alleles using a theoretical model based on molecular dynamics simulations. The fluctuational entropies of the peptides are estimated over a temperature range of 310-460 K. The estimated entropies correlate well with experimental binding affinities of the peptides: peptides that have higher binding affinities have lower entropies compared to non-binders, which have significantly larger entropies. The computation of the entropies is based on a simple model that requires short molecular dynamics trajectories and allows for approximate but rapid determination. The paper draws attention to the long neglected dynamic aspects of peptide binding, and provides a fast computation scheme that allows for rapid scanning of large numbers of peptides on selected HLA antigens, which may be useful in defining the right peptides for personal immunotherapy.

Entropy Transfer between Residue Pairs and Allostery in Proteins: Quantifying Allosteric Communication in Ubiquitin.

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.

Molecular dynamics simulations of site point mutations in the TPR domain of cyclophilin 40 identify conformational states with distinct dynamic and enzymatic properties.

Cyclophilin 40 (Cyp40) is a member of the immunophilin family that acts as a peptidyl-prolyl-isomerase enzyme and binds to the heat shock protein 90 (Hsp90). Its structure comprises an N-terminal cyclophilin domain and a C-terminal tetratricopeptide (TPR) domain. Cyp40 is overexpressed in prostate cancer and certain T-cell lymphomas. The groove for Hsp90 binding on the TPR domain includes residues Lys227 and Lys308, referred to as the carboxylate clamp, and is essential for Cyp40-Hsp90 binding. In this study, the effect of two mutations, K227A and K308A, and their combinative mutant was investigated by performing a total of 5.76 µs of all-atom molecular dynamics (MD) simulations in explicit solvent. All simulations, except the K308A mutant, were found to adopt two distinct (extended or compact) conformers defined by different cyclophilin-TPR interdomain distances. The K308A mutant was only observed in the extended form which is observed in the Cyp40 X-ray structure. The wild-type, K227A, and combined mutant also showed bimodal distributions. The experimental melting temperature, Tm, values of the mutants correlate with the degree of compactness with the K308A extended mutant having a marginally lower melting temperature. Another novel measure of compactness determined from the MD data, the "coordination shell volume," also shows a direct correlation with Tm. In addition, the MD simulations show an allosteric effect with the mutations in the remote TPR domain having a pronounced effect on the molecular motions of the enzymatic cyclophilin domain which helps rationalise the experimentally observed increase in enzyme activity measured for all three mutations.

Causality, transfer entropy, and allosteric communication landscapes in proteins with harmonic interactions.

A fast and approximate method of generating allosteric communication landscapes in proteins 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 an ensemble of pathways is possible. The model emphasizes that knowledge of entropy only is not sufficient for determining allosteric communication and additional information based on time delayed correlations should 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. By this approach, residues that should be manipulated to control protein activity may be determined. This should be of great importance for allosteric drug design and for understanding the effects of mutations on function. The model is applied to determine allosteric communication in three proteins, Ubiquitin, Pyruvate Kinase, and the PDZ domain. Predictions are in agreement with molecular dynamics simulations and experimental evidence. Proteins 2017; 85:1056-1064. © 2017 Wiley Periodicals, Inc.

Reducing Virulence and Biofilm of Pseudomonas aeruginosa by Potential Quorum Sensing Inhibitor Carotenoid: Zeaxanthin.

Pseudomonas aeruginosa can regulate its virulence gene expressions by using a signal system called quorum sensing. It is known that inhibition of quorum sensing can block biofilm formation and leave the bacteria defenseless. Therefore, it is necessary to determine natural sources to obtain potential quorum sensing inhibitors. This study aims to investigate an alternative treatment approach by utilizing the carotenoid zeaxanthin to reduce the expressions of P. aeruginosa virulence factors through quorum sensing inhibition. The inhibition potential of zeaxanthin was determined by in silico screening from a library of 638 lichen metabolites. Fluorescent monitor strains were utilized for quorum sensing inhibitor screens, and quantitative reverse-transcriptase PCR assay was performed for evaluating gene expression. Results indicate that zeaxanthin is a better inhibitor than the lichen secondary metabolite evernic acid, which was previously shown to be capable of inhibiting P. aeruginosa quorum sensing systems.

Universal features of fluctuations in globular proteins.

Using data from 2000 non-homologous protein crystal structures, we show that the distribution of residue B factors of proteins collapses onto a single master curve. We show by maximum entropy arguments that this curve is a Gamma function whose order and dispersion are obtained from experimental data. The distribution for any given specific protein can be generated from the master curve by a linear transformation. Any perturbation of the B factor distribution of a protein, imposed at constant energy, causes a decrease in the entropy of the protein relative to that of the reference state. Proteins 2016; 84:721-725. © 2016 Wiley Periodicals, Inc.

A Molecular Dynamics Study of Allosteric Transitions in Leishmania mexicana Pyruvate Kinase.

A comparative molecular dynamics analysis of the pyruvate kinase from Leishmania mexicana is presented in the absence and presence of the allosteric effector fructose 2,6-bisphosphate. Comparisons of the simulations of the large 240 kDa apo and holo tetramers show that binding of fructose 2,6-bisphosphate cools the enzyme and reduces dynamic movement, particularly of the B-domain. The reduced dynamic movement of the holo form traps the pyruvate kinase tetramer in its enzymatically active state with the B-domain acting as a lid to cover the active site. The simulations are also consistent with a transition of the mobile active-site α6' helix, which would adopt a helical conformation in the active R-state and a less structured coil conformation in the inactive T-state. Analysis of the rigid body motions over the trajectory highlights the concerted anticorrelated rigid body rocking motion of the four protomers, which drives the T to R transition. The transitions predicted by these simulations are largely consistent with the Monod-Wyman-Changeux model for allosteric activation but also suggest that rigidification or cooling of the overall structure upon effector binding plays an additional role in enzyme activation.

Effects of ligand binding upon flexibility of proteins.

Binding of a ligand on a protein changes the flexibility of certain parts of the protein, which directly affects its function. These changes are not the same at each point, some parts become more flexible and some others become stiffer. Here, an equation is derived that gives the stiffness map for proteins. The model is based on correlations of fluctuations of pairs of points in proteins, which may be evaluated at different levels of refinement, ranging from all atom molecular dynamics to general elastic network models, including the simplest case of isotropic Gaussian Network Model. The latter is used, as an example, to evaluate the changes of stiffness upon dimerization of ACK1.