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.

Computational analysis of long-range allosteric communications in CFTR.

Malfunction of the CFTR protein results in cystic fibrosis, one of the most common hereditary diseases. CFTR functions as an anion channel, the gating of which is controlled by long-range allosteric communications. Allostery also has direct bearings on CF treatment: the most effective CFTR drugs modulate its activity allosterically. Herein, we integrated Gaussian network model, transfer entropy, and anisotropic normal mode-Langevin dynamics and investigated the allosteric communications network of CFTR. The results are in remarkable agreement with experimental observations and mutational analysis and provide extensive novel insight. We identified residues that serve as pivotal allosteric sources and transducers, many of which correspond to disease-causing mutations. We find that in the ATP-free form, dynamic fluctuations of the residues that comprise the ATP-binding sites facilitate the initial binding of the nucleotide. Subsequent binding of ATP then brings to the fore and focuses on dynamic fluctuations that were present in a latent and diffuse form in the absence of ATP. We demonstrate that drugs that potentiate CFTR's conductance do so not by directly acting on the gating residues, but rather by mimicking the allosteric signal sent by the ATP-binding sites. We have also uncovered a previously undiscovered allosteric 'hotspot' located proximal to the docking site of the phosphorylated regulatory (R) domain, thereby establishing a molecular foundation for its phosphorylation-dependent excitatory role. This study unveils the molecular underpinnings of allosteric connectivity within CFTR and highlights a novel allosteric 'hotspot' that could serve as a promising target for the development of novel therapeutic interventions.

Subsets of Slow Dynamic Modes Reveal Global Information Sources as Allosteric Sites.

Allostery is a key biological control mechanism, and dynamic information flow provides a perspective to describe allosteric interactions in causal relationships. Here, as a novel implementation of the Gaussian Network Model (GNM) based Transfer Entropy (TE) calculations, we show that the dissection of dynamic information into subsets of slow dynamic modes discloses different layers of multi-directional allosteric pathways inherent in a given protein structure. In these subsets of slow modes, the degree of collectivity (Col) in the information transfer of residues with their TE values (TECol score) identifies distinct residues as powerful effectors, global information sources; showing themselves with a high dynamic capacity to collectively disseminate information to others. As exemplified on aspartate transcarbamoylase (ATCase), Na+/K+-adenosine triphosphatase (Na+/K+-ATPase), and human transient receptor potential melastatin 2 (TRPM2) along with a dataset of 20 proteins, these specific residues are associated with known active and allosteric sites. These information source residues, which collectively control others and lead allosteric communication pathways, hint at plausible binding sites for structure-based rational drug design.

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.

Structural insight into host plasma membrane association and assembly of HIV-1 matrix protein.

Oligomerization of Pr55Gag is a critical step of the late stage of the HIV life cycle. It has been known that the binding of IP6, an abundant endogenous cyclitol molecule at the MA domain, has been linked to the oligomerization of Pr55Gag. However, the exact binding site of IP6 on MA remains unknown and the structural details of this interaction are missing. Here, we present three high-resolution crystal structures of the MA domain in complex with IP6 molecules to reveal its binding mode. Additionally, extensive Differential Scanning Fluorimetry analysis combined with cryo- and ambient-temperature X-ray crystallography and GNM-based transfer entropy calculations identify the key residues that participate in IP6 binding. Our data provide novel insights about the multilayered HIV-1 virion assembly process that involves the interplay of IP6 with PIP2, a phosphoinositide essential for the binding of Pr55Gag to membrane. IP6 and PIP2 have neighboring alternate binding sites within the same highly basic region (residues 18-33). This indicates that IP6 and PIP2 bindings are not mutually exclusive and may play a key role in coordinating virion particles' membrane localization. Based on our three different IP6-MA complex crystal structures, we propose a new model that involves IP6 coordination of the oligomerization of outer MA and inner CA domain's 2D layers during assembly and budding.

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.

Protein dynamics analysis identifies candidate cancer driver genes and mutations in TCGA data.

Recently, it has been showed that cancer missense mutations selectively target the neighborhood of hinge residues, which are key sites in protein dynamics. Here, we show that this approach can be extended to find previously unknown candidate mutations and genes. To this aim, we developed a computational pipeline to detect significantly enriched three-dimensional (3D) clustering of missense mutations around hinge residues. The hinge residues were detected by applying a Gaussian network model. By systematically analyzing the PanCancer compendium of somatic mutations in nearly 10 000 tumors from the Cancer Genome Atlas, we identified candidate genes and mutations in addition to well known ones. For instance, we found significantly enriched 3D clustering of missense mutations in known cancer genes including CDK4, CDKN2A, TCL1A, and MAPK1. Beside these known genes, we also identified significantly enriched 3D clustering of missense mutations around hinge residues in PLA2G4A, which may lead to excessive phosphorylation of the extracellular signal-regulated kinases. Furthermore, we demonstrated that hinge-based features improves pathogenicity prediction for missense mutations. Our results show that the consideration of clustering around hinge residues can help us explain the functional role of the mutations in known cancer genes and identify candidate genes.

Oncogenic mutations on Rac1 affect global intrinsic dynamics underlying GTP and PAK1 binding.

Rac1 is a small member of the Rho GTPase family. One of the most important downstream effectors of Rac1 is a serine/threonine kinase, p21-activated kinase 1 (PAK1). Mutational activation of PAK1 by Rac1 has oncogenic signaling effects. Here, although we focus on Rac1-PAK1 interaction by atomic-force-microscopy-based single-molecule force spectroscopy experiments, we explore the effect of active mutations on the intrinsic dynamics and binding interactions of Rac1 by Gaussian network model analysis and molecular dynamics simulations. We observe that Rac1 oncogenic mutations are at the hinges of three global modes of motion, suggesting the mechanical changes as potential markers of oncogenicity. Indeed, the dissociation of wild-type Rac1-PAK1 complex shows two distinct unbinding dynamic states that are reduced to one with constitutively active Q61L and oncogenic Y72C mutant Rac1, as revealed by single-molecule force spectroscopy experiments. Q61L and Y72C mutations change the mechanics of the Rac1-PAK1 complex by increasing the elasticity of the protein and slowing down the transition to the unbound state. On the other hand, Rac1's intrinsic dynamics reveal more flexible GTP and PAK1-binding residues on switches I and II with Q61L, Y72C, oncogenic P29S and Q61R, and negative T17N mutations. The cooperativity in the fluctuations of GTP-binding sites around the p-loop and switch I decreases in all mutants, mostly in Q61L, whereas some PAK1-binding residues display enhanced coupling with GTP-binding sites in Q61L and Y72C and within each other in P29S. The predicted binding free energies of the modeled Rac1-PAK1 complexes show that the change in the dynamic behavior likely means a more favorable PAK1 interaction. Overall, these findings suggest that the active mutations affect intrinsic functional dynamic events and alter the mechanics underlying the binding of Rac1 to GTP and upstream and downstream partners including PAK1.

Local and Global Motions Underlying Antibiotic Binding in Bacterial Ribosome.

The bacterial ribosome is one of the most important targets in the treatment of infectious diseases. As antibiotic resistance in bacteria poses a growing threat, a significant amount of effort is concentrated on exploring new drug-binding sites where testable predictions are of significance. Here, we study the dynamics of a ribosomal complex and 67 small and large subunits of the ribosomal crystal structures (64 antibiotic-bound, 3 antibiotic-free) from Deinococcus radiodurans, Escherichia coli, Haloarcula marismortui, and Thermus thermophilus by the Gaussian network model. Interestingly, a network of nucleotides coupled in high-frequency fluctuations reveals known antibiotic-binding sites. These sites are seen to locate at the interface of dynamic domains that have an intrinsic dynamic capacity to interfere with functional globular motions. The nucleotides and the residues fluctuating in the fast and slow modes of motion thus have promise for plausible antibiotic-binding and allosteric sites that can alter antibiotic binding and resistance. Overall, the present analysis brings a new dynamic perspective to the long-discussed link between small-molecule binding and large conformational changes of the supramolecule.

Distinct Allosteric Networks Underlie Mechanistic Speciation of ABC Transporters.

ABC transporters couple the energy of ATP hydrolysis to the transmembrane transport of biomolecules. Here, we investigated the allosteric networks of three representative ABC transporters using a hybrid molecular simulations approach validated by experiments. Each of the three transporters uses a different allosteric network: in the constitutive B12 importer BtuCD, ATP binding is the main driver of allostery and docking/undocking of the substrate-binding protein (SBP) is the driven event. The allosteric signal originates at the cytoplasmic side of the membrane before propagating to the extracellular side. In the substrate-controlled maltose transporter, the SBP is the main driver of allostery, ATP binding is the driven event, and the allosteric signal propagates from the extracellular to the cytoplasmic side of the membrane. In the lipid flippase PglK, a cyclic crosstalk between ATP and substrate binding underlies allostery. These results demonstrate speciation of biological functions may arise from variations in allosteric connectivity.

Protein dynamics analysis reveals that missense mutations in cancer-related genes appear frequently on hinge-neighboring residues.

Missense mutations have various effects on protein structures, also leading to distorted protein dynamics that plausibly affects the function. We hypothesized that missense mutations in cancer-related genes selectively target hinge-neighboring residues that orchestrate collective structural dynamics. To test our hypothesis, we selected 69 cancer-related genes from the Cancer Gene Census database and their representative protein structures from the Protein Data Bank. We first identified the hinge residues in two global modes of motion by applying the Gaussian Network Model. We then showed that missense mutations are significantly enriched on hinge-neighboring residues in oncogenes and tumor suppressor genes. We observed that several oncogenes (eg, MAP2K1, PTPN11, and KRAS) and tumor suppressor genes (eg, EZH2, CDKN2C, and RHOA) strongly exhibit this phenomenon. This study highlights and rationalizes the functional importance of missense mutations on hinge-neighboring residues in cancer.

Single-molecule probing of the conformational homogeneity of the ABC transporter BtuCD.

ATP-binding cassette (ABC) transporters use the energy of ATP hydrolysis to move molecules through cellular membranes. They are directly linked to human diseases, cancer multidrug resistance, and bacterial virulence. Very little is known of the conformational dynamics of ABC transporters, especially at the single-molecule level. Here, we combine single-molecule spectroscopy and a novel molecular simulation approach to investigate the conformational dynamics of the ABC transporter BtuCD. We observe a single dominant population of molecules in each step of the transport cycle and tight coupling between conformational transitions and ligand binding. We uncover transient conformational changes that allow substrate to enter the transporter. This is followed by a 'squeezing' motion propagating from the extracellular to the intracellular side of the translocation cavity. This coordinated sequence of events provides a mechanism for the unidirectional transport of vitamin B12 by BtuCD.

Cullin neddylation may allosterically tune polyubiquitin chain length and topology.

Conjugation of Nedd8 (neddylation) to Cullins (Cul) in Cul-RING E3 ligases (CRLs) stimulates ubiquitination and polyubiquitination of protein substrates. CRL is made up of two Cul-flanked arms: one consists of the substrate-binding and adaptor proteins and the other consists of E2 and Ring-box protein (Rbx). Polyubiquitin chain length and topology determine the substrate fate. Here, we ask how polyubiquitin chains are accommodated in the limited space available between the two arms and what determines the polyubiquitin linkage topology. We focus on Cul5 and Rbx1 in three states: before Cul5 neddylation (closed state), after neddylation (open state), and after deneddylation, exploiting molecular dynamics simulations and the Gaussian Network Model. We observe that regulation of substrate ubiquitination and polyubiquitination takes place through Rbx1 rotations, which are controlled by Nedd8-Rbx1 allosteric communication. Allosteric propagation proceeds from Nedd8 via Cul5 dynamic hinges and hydrogen bonds between the C-terminal domain of Cul5 (Cul5CTD) and Rbx1 (Cul5CTD residues R538/R569 and Rbx1 residue E67, or Cul5CTD E474/E478/N491 and Rbx1 K105). Importantly, at each ubiquitination step (homogeneous or heterogeneous, linear or branched), the polyubiquitin linkages fit into the distances between the two arms, and these match the inherent CRL conformational tendencies. Hinge sites may constitute drug targets.

DynaFace: Discrimination between Obligatory and Non-obligatory Protein-Protein Interactions Based on the Complex's Dynamics.

Protein-protein interfaces have been evolutionarily-designed to enable transduction between the interacting proteins. Thus, we hypothesize that analysis of the dynamics of the complex can reveal details about the nature of the interaction, and in particular whether it is obligatory, i.e., persists throughout the entire lifetime of the proteins, or not. Indeed, normal mode analysis, using the Gaussian network model, shows that for the most part obligatory and non-obligatory complexes differ in their decomposition into dynamic domains, i.e., the mobile elements of the protein complex. The dynamic domains of obligatory complexes often mix segments from the interacting chains, and the hinges between them do not overlap with the interface between the chains. In contrast, in non-obligatory complexes the interface often hinges between dynamic domains, held together through few anchor residues on one side of the interface that interact with their counterpart grooves in the other end. In automatic analysis, 117 of 139 obligatory (84.2%) and 203 of 246 non-obligatory (82.5%) complexes are correctly classified by our method: DynaFace. We further use DynaFace to predict obligatory and non-obligatory interactions among a set of 300 putative protein complexes. DynaFace is available at: http://safir.prc.boun.edu.tr/dynaface.

NhaA antiporter functions using 10 helices, and an additional 2 contribute to assembly/stability.

The Escherichia coli Na(+)/H(+) antiporter (Ec-NhaA) is the best-characterized of all pH-regulated Na(+)/H(+) exchangers that control cellular Na(+) and H(+) homeostasis. Ec-NhaA has 12 helices, 2 of which (VI and VII) are absent from other antiporters that share the Ec-NhaA structural fold. This α-hairpin is located in the dimer interface of the Ec-NhaA homodimer together with a ß-sheet. Here we examine computationally and experimentally the role of the α-hairpin in the stability, dimerization, transport, and pH regulation of Ec-NhaA. Evolutionary analysis (ConSurf) indicates that the VI-VII helical hairpin is much less conserved than the remaining transmembrane region. Moreover, normal mode analysis also shows that intact NhaA and a variant, deleted of the α-hairpin, share similar dynamics, suggesting that the structure may be dispensable. Thus, two truncated Ec-NhaA mutants were constructed, one deleted of the α-hairpin and another also lacking the ß-sheet. The mutants were studied at physiological pH in the membrane and in detergent micelles. The findings demonstrate that the truncated mutants retain significant activity and regulatory properties but are defective in the assembly/stability of the Ec-NhaA dimer.

Allosteric Dynamic Control of Binding.

Proteins have a highly dynamic nature and there is a complex interrelation between their structural dynamics and binding behavior. By assuming various conformational ensembles, they perform both local and global fluctuations to interact with other proteins in a dynamic infrastructure adapted to functional motion. Here, we show that there is a significant association between allosteric mutations, which lead to high-binding-affinity changes, and the hinge positions of global modes, as revealed by a large-scale statistical analysis of data in the Structural Kinetic and Energetic Database of Mutant Protein Interactions (SKEMPI). We further examined the mechanism of allosteric dynamics by conducting studies on human growth hormone (hGH) and pyrin domain (PYD), and the results show how mutations at the hinge regions could allosterically affect the binding-site dynamics or induce alternative binding modes by modifying the ensemble of accessible conformations. The long-range dissemination of perturbations in local chemistry or physical interactions through an impact on global dynamics can restore the allosteric dynamics. Our findings suggest a mechanism for the coupling of structural dynamics to the modulation of protein interactions, which remains a critical phenomenon in understanding the effect of mutations that lead to functional changes in proteins.

Adaptability of protein structures to enable functional interactions and evolutionary implications.

Several studies in recent years have drawn attention to the ability of proteins to adapt to intermolecular interactions by conformational changes along structure-encoded collective modes of motions. These so-called soft modes, primarily driven by entropic effects, facilitate, if not enable, functional interactions. They represent excursions on the conformational space along principal low-ascent directions/paths away from the original free energy minimum, and they are accessible to the protein even before protein-protein/ligand interactions. An emerging concept from these studies is the evolution of structures or modular domains to favor such modes of motion that will be recruited or integrated for enabling functional interactions. Structural dynamics, including the allosteric switches in conformation that are often stabilized upon formation of complexes and multimeric assemblies, emerge as key properties that are evolutionarily maintained to accomplish biological activities, consistent with the paradigm sequence→structure→dynamics→function where 'dynamics' bridges structure and function.

Changes to the dynamic nature of hemagglutinin and the emergence of the 2009 pandemic H1N1 influenza virus.

The virologic factors that limit the transmission of swine influenza viruses between humans are unresolved. While it has been shown that acquisition of the neuraminidase (NA) and matrix (M) gene segments from a Eurasian-lineage swine virus was required for airborne transmission of the 2009 pandemic H1N1 virus (H1N1pdm09), we show here that an arginine to lysine change in the hemagglutinin (HA) was also necessary. This change at position 149 was distal to the receptor binding site but affected virus-receptor affinity and HA dynamics, allowing the virus to replicate more efficiently in nasal turbinate epithelium and subsequently transmit between ferrets. Receptor affinity should be considered as a factor limiting swine virus spread in humans.

Drug-resistant HIV-1 protease regains functional dynamics through cleavage site coevolution.

Drug resistance is caused by mutations that change the balance of recognition favoring substrate cleavage over inhibitor binding. Here, a structural dynamics perspective of the regained wild-type functioning in mutant HIV-1 proteases with coevolution of the natural substrates is provided. The collective dynamics of mutant structures of the protease bound to p1-p6 and NC-p1 substrates are assessed using the Anisotropic Network Model (ANM). The drug-induced protease mutations perturb the mechanistically crucial hinge axes that involve key sites for substrate binding and dimerization and mainly coordinate the intrinsic dynamics. Yet with substrate coevolution, while the wild-type dynamic behavior is restored in both p1-p6 ((LP) (1'F)p1-p6D30N/N88D) and NC-p1 ((AP) (2) (V)NC-p1V82A) bound proteases, the dynamic behavior of the NC-p1 bound protease variants (NC-p1V82A and (AP) (2) (V)NC-p1V82A) rather resemble those of the proteases bound to the other substrates, which is consistent with experimental studies. The orientational variations of residue fluctuations along the hinge axes in mutant structures justify the existence of coevolution in p1-p6 and NC-p1 substrates, that is, the dynamic behavior of hinge residues should contribute to the interdependent nature of substrate recognition. Overall, this study aids in the understanding of the structural dynamics basis of drug resistance and evolutionary optimization in the HIV-1 protease system.