Essential dynamics sampling study of adenylate kinase: comparison to citrate synthase and implication for the hinge and shear mechanisms of domain motions

Essential dynamics sampling simulations of the domain conformations of unliganded Escherichia coli adenylate kinase have been performed to determine whether the ligand-induced closed-domain conformation is accessible to the open unliganded enzyme. Adenylate kinase is a three- domain protein with a central CORE domain and twoflanking domains, the LID and the NMPbind domains. The sampling simulations were applied to the CORE and NMPbind domain pair and the CORE and LID domain pair separately. One aim is to compare the results to those of a similar study on the enzyme citrate synthase to determine whether a similar domain-locking mechanism operates in adenylate kinase. Although for adenylate kinase the simulations suggest that the closed-domain conformation of the unliganded enzyme is at a slightly higher free energy than the open for both domain pairs, the results are radically different to those found for citrate synthase. In adenylate kinase the targeted domain conformations could always be achieved, whereas this was not the case in citrate synthase due to an apparent free-energy barrier between the open and closed conformations. Adenylate kinase has been classified as a protein that undergoes closure through a hinge mechanism, whereas citrate synthase has been assigned to the shear mechanism. This was quantified here in terms of the change in the number of interdomain contacting atoms upon closure which showed a considerable increase in adenylate kinase. For citrate synthase this number remained largely the same, suggesting that the domain faces slide over each other during closure. This suggests that shear and hinge mechanisms of domain closure may relate to the existence or absence of an appreciable barrier to closure for the unliganded protein, as the latter can hinge comparatively freely, whereas the former must follow a more constrained path. In general though it appears a bias toward keeping the unliganded enzyme in the open-domain conformation may be a common feature of domain enzymes.     

Substrate binding and catalytic mechanism in phospholipase C from Bacillus Cereus: A molecular mechanics and molecular dynamics study

For the first time a consistent catalytic mechanism of phospholipase C from Bacillus cereus is reported based on molecular mechanics calculations. We have identified the position of the nucleophilic water molecule, which is directly involved in the hydrolysis of the natural substrate, phosphatidylcholine, in phospholipase C. This catalytically essential water molecule, after being activated by an acidic residue (Asp55), performs the nucleophilic attack on the phosphorus atom in the substrate, leading to a trigonal bipyramidal pentacoordinated intermediate (and structurally similar transition state). The subsequent collapse of the intermediate, regeneration of the enzyme, and release of the products has to involve a not yet identified second water molecule. The catalytic mechanism reported here is based on a series of molecular mechanics calculations. First, the x-ray structure of phospholipase C from B. cereus including a docked substrate molecule was subjected to a stepwise molecular mechanics energy minimization. Second, the location of the nucleophilic water molecule in the active site of the fully relaxed enzyme–substrate complex was determined by evaluation of nonbonded interaction energies between the complex and a water molecule. The nucleophilic water molecule is positioned at a distance (3.8 Å) from the phosphorus atom in the substrate, which is in good agreement with experimentally observed distances. Finally, the stability of the complex between phospholipase C, the substrate, and the nucleophilic water molecule was verified during a 100 ps molecular dynamics simulation. During the simulation the substrate undergoes a conformational change, but retains its localization in the active site. The contacts between the enzyme, the substrate, and the nucleophilic water molecule display some fluctuations, but remain within reasonable limits, thereby confirming the stability of the enzyme–substrate–water complex. The protocol developed for energy minimization of phospholipase C containing three zinc ions located closely together at the bottom of the active site cleft is reported in detail. In order to handle the strong electrostatic interactions in the active site realistically during energy minimization, delocalization of the charges from the three zinc ions was considered. Therefore, quantum mechanics calculations on the zinc ions and the zinc-coordinating residues were carried out prior to the molecular mechanics calculations, and two different sets of partial atomic charges (MNDO-Mulliken and AM1-ESP) were applied. After careful assignment of partial atomic charges, a complete energy minimization of the protein was carried out by a stepwise procedure without explicit solvent molecules. Energy minimization with either set of charges yielded structures, which were very similar both to the x-ray structure and to each other, although using AM1-ESP partial atomic charges and a dielectric constant of 4, yielded the best protein structure. © 1997 John Wiley and Sons, Inc. Biopoly 42: 319–336, 1997     

Substrate binding to Src: A new perspective on tyrosine kinase substrate recognition from NMR and molecular dynamics

Most signal transduction pathways in humans are regulated by protein kinases through phosphorylation of their protein substrates. Typical eukaryotic protein kinases are of two major types: those that phosphorylate‐specific sequences containing tyrosine (~90 kinases) and those that phosphorylate either serine or threonine (~395 kinases). The highly conserved catalytic domain of protein kinases comprises a smaller N lobe and a larger C lobe separated by a cleft region lined by the activation loop. Prior studies find that protein tyrosine kinases recognize peptide substrates by binding the polypeptide chain along the C‐lobe on one side of the activation loop, while serine/threonine kinases bind their substrates in the cleft and on the side of the activation loop opposite to that of the tyrosine kinases. Substrate binding structural studies have been limited to four families of the tyrosine kinase group, and did not include Src tyrosine kinases. We examined peptide‐substrate binding to Src using paramagnetic‐relaxation‐enhancement NMR combined with molecular dynamics simulations. The results suggest Src tyrosine kinase can bind substrate positioning residues C‐terminal to the phosphoacceptor residue in an orientation similar to serine/threonine kinases, and unlike other tyrosine kinases. Mutagenesis corroborates this new perspective on tyrosine kinase substrate recognition. Rather than an evolutionary split between tyrosine and serine/threonine kinases, a change in substrate recognition may have occurred within the TK group of the human kinome. Protein tyrosine kinases have long been therapeutic targets, but many marketed drugs have deleterious off‐target effects. More accurate knowledge of substrate interactions of tyrosine kinases has the potential for improving drug selectivity.     

Effect of DNA on the conformational dynamics of the endonucleases I‐DmoI as provided by molecular dynamics simulations

The conformational behavior of the wild‐type endonucleases I‐DmoI and two of its mutants has been studied in the presence and in the absence of DNA target sequences by means of extended molecular dynamics simulations. Our results show that in the absence of DNA, the three protein forms explore a similar essential conformational space, whereas when bound to the same DNA target sequence of 25 base pairs, they diversify and restrain the subspace explored. In addition, the differences in the essential subspaces explored by the residues near the catalytic site for both the bound and unbound forms are discussed in background of the experimental protein activity.     

Domain motions in bacteriophage T4 lysozyme: A comparison between molecular dynamics and crystallographic data

A comparison of a series of extended molecular dynamics (MD) simulations of bacteriophage T4 lysozyme in solvent with X-ray data is presented. Essential dynamics analyses were used to derive collective fluctuations from both the simulated trajectories and a distribution of crystallographic conformations. In both cases the main collective fluctuations describe domain motions. The protein consists of an N- and C-terminal domain connected by a long helix. The analysis of the distribution of crystallographic conformations reveals that the N-terminal helix rotates together with either of these two domains. The main domain fluctuation describes a closure mode of the two domains in which the N-terminal helix rotates concertedly with the C-terminal domain, while the domain fluctuation with second largest amplitude corresponds to a twisting mode of the two domains, with the N-terminal helix rotating concertedly with the N-terminal domain. For the closure mode, the difference in hinge-bending angle between the most open and most closed X-ray structure along this mode is 49 degrees. In the MD simulation that shows the largest fluctuation along this mode, a rotation of 45 degrees was observed. Although the twisting mode has much less freedom than the closure mode in the distribution of crystallographic conformations, experimental results suggest that it might be functionally important. Interestingly, the twisting mode is sampled more extensively in all MD simulations than it is in the distribution of X-ray conformations. Proteins 31:116–127, 1998. © 1998 Wiley-Liss, Inc.     

pH‐dependent conformational dynamics of beta‐secretase 1: A molecular dynamics study

Beta‐secretase 1 (BACE‐1) is an aspartyl protease implicated in the overproduction of β‐amyloid fibrils responsible for Alzheimer disease. The process of β‐amyloid genesis is known to be pH dependent, with an activity peak between solution pH of 3.5 and 5.5. We have studied the pH‐dependent dynamics of BACE‐1 to better understand the pH dependent mechanism. We have implemented support for graphics processor unit (GPU) accelerated constant pH molecular dynamics within the AMBER molecular dynamics software package and employed this to determine the relative population of different aspartyl dyad protonation states in the pH range of greatest β‐amyloid production, followed by conventional molecular dynamics to explore the differences among the various aspartyl dyad protonation states. We observed a difference in dynamics between double‐protonated, mono‐protonated, and double‐deprotonated states over the known pH range of higher activity. These differences include Tyr 71‐aspartyl dyad proximity and active water lifetime. This work indicates that Tyr 71 stabilizes catalytic water in the aspartyl dyad active site, enabling BACE‐1 activity.     

Insights into the binding specificity of wild type and mutated wheat germ agglutinin towards Neu5Acα(2‐3)Gal: a study by in silico mutations and molecular dynamics simulations

Wheat germ agglutinin (WGA) is a plant lectin, which specifically recognizes the sugars NeuNAc and GlcNAc. Mutated WGA with enhanced binding specificity can be used as biomarkers for cancer. In silico mutations are performed at the active site of WGA to enhance the binding specificity towards sialylglycans, and molecular dynamics simulations of 20 ns are carried out for wild type and mutated WGAs (WGA1, WGA2, and WGA3) in complex with sialylgalactose to examine the change in binding specificity. MD simulations reveal the change in binding specificity of wild type and mutated WGAs towards sialylgalactose and bound conformational flexibility of sialylgalactose. The mutated polar amino acid residues Asn114 (S114N), Lys118 (G118K), and Arg118 (G118R) make direct and water mediated hydrogen bonds and hydrophobic interactions with sialylgalactose. An analysis of possible hydrogen bonds, hydrophobic interactions, total pair wise interaction energy between active site residues and sialylgalactose and MM‐PBSA free energy calculation reveals the plausible binding modes and the role of water in stabilizing different binding modes. An interesting observation is that the binding specificity of mutated WGAs (cyborg lectin) towards sialylgalactose is found to be higher in double point mutation (WGA3). One of the substituted residues Arg118 plays a crucial role in sugar binding. Based on the interactions and energy calculations, it is concluded that the order of binding specificity of WGAs towards sialylgalactose is WGA3 > WGA1 > WGA2 > WGA. On comparing with the wild type, double point mutated WGA (WGA3) exhibits increased specificity towards sialylgalactose, and thus, it can be effectively used in targeted drug delivery and as biological cell marker in cancer therapeutics. Copyright © 2014 John Wiley & Sons, Ltd.     

A principal component analysis of the dynamics of subdomains and binding sites in human serum albumin

The conformational dynamics of human serum albumin (HSA) was investigated by principal component analysis (PCA) applied to three molecular dynamics trajectories of 200 ns each. The overlap of the essential subspaces spanned by the first 10 principal components (PC) of different trajectories was about 0.3 showing that the PCA based on a trajectory length of 200 ns is not completely convergent for this protein. The contributions of the relative motion of subdomains and of the subdomains (internal) distortion to the first 10 PCs were found to be comparable. Based on the distribution of the first 3 PC, 10 protein conformers are identified showing relative root mean square deviations (RMSD) between 2.3 and 4.6 Å. The main PCs are found to be delocalized over the whole protein structure indicating that the motions of different protein subdomains are coupled. This coupling is considered as being related to the allosteric effects observed upon ligand binding to HSA. On the other hand, the first PC of one of the three trajectories describes a conformational transition of the protein domain I that is close to that experimentally observed upon myristate binding. This is a theoretical support for the older hypothesis stating that changes of the protein onformation favorable to binding can precede the ligand complexation. A detailed all atoms PCA performed on the primary Sites 1 and 2 confirms the multiconformational character of the HSA binding sites as well as the significant coupling of their motions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 561–572, 2014.     

Investigating the binding of β‐1,4‐galactan to Bacillus licheniformis β‐1,4‐galactanase by crystallography and computational modeling

Microbial β‐1,4‐galactanases are glycoside hydrolases belonging to family 53, which degrade galactan and arabinogalactan side chains in the hairy regions of pectin, a major plant cell wall component. They belong to the larger clan GH‐A of glycoside hydrolases, which cover many different poly‐ and oligosaccharidase specificities. Crystallographic complexes of Bacillus licheniformis β‐1,4‐galactanase and its inactive nucleophile mutant have been obtained with methyl‐β(1→4)‐galactotetraoside, providing, for the first time, information on substrate binding to the aglycone side of the β‐1,4‐galactanase substrate binding groove. Using the experimentally determined subsites as a starting point, a β(1→4)‐galactononaose was built into the structure and subjected to molecular dynamics simulations giving further insight into the residues involved in the binding of the polysaccharide from subsite ?4 to +5. In particular, this analysis newly identified a conserved β‐turn, which contributes to subsites ?2 to +3. This β‐turn is unique to family 53 β‐1,4‐galactanases among all clan GH‐A families that have been structurally characterized and thus might be a structural signature for endo‐β‐1,4‐galactanase specificity. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

The role of the Val57 amino‐acid residue in the hinge loop of the human cystatin C. Conformational studies of the beta2‐L1‐beta3 segments of wild‐type human cystatin C and its mutants

Human cystatin C (HCC) is one of the amyloidogenic proteins to be shown to oligomerize via a three‐dimensional domain swapping mechanism. This process precedes the formation of a stable dimer and proceeds particularly easily in the case of the L68Q mutant. According to the proposed mechanism, dimerization of the HCC precedes conformational changes within the β2 and β3 strands. In this article, we present conformational studies, using circular dichroism and MD methods, of the β2‐L1‐β3 (His43‐Thr72) fragment of the HCC involved in HCC dimer formation. We also carried out studies of the β2‐L1‐β3 peptide, in which the Val57 residue was replaced by residues promoting β‐turn structure formation (Asp, Asn, or Pro). The present study established that point mutation could modify the structure of the L1 loop in the β‐hairpin peptide. Our results showed that the L1 loop in the peptide excised from human cystatin C is broader than that in cystatin C. In the HCC protein, broadening of the L1 loop together with the unfavorable L68Q mutation in the hydrophobic pocket could be a force sufficient to cause the partial unfolding and then the opening of HCC or its L68Q mutant structure for further dimerization. We presume further that the Asp57 and Asn57 mutations in the L1 loop of HCC could stabilize the closed form of HCC, whereas the Pro57 mutation could lead to the opening of the HCC structure and then to dimer/oligomer formation. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 373–383, 2009. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Deprotonation states of the two active site water molecules regulate the binding of protein phosphatase 5 with its substrate: A molecular dynamics study

Protein phosphatase 5 (PP5), mainly localized in human brain, can dephosphorylate tau protein whose high level of phosphorylation is related to Alzheimer's disease. Similar to other protein phosphatases, PP5 has a conserved motif in the catalytic domain that contains two binding sites for manganese (Mn²⁺) ions. Structural data indicate that two active site water molecules, one bridging the two Mn²⁺ ions and the other terminally coordinated with one of the Mn²⁺ ions (Mn1), are involved in catalysis. Recently, a density functional theory study revealed that the two water molecules can be both deprotonated to keep a neutral active site for catalysis. The theoretical study gives us an insight into the catalytic mechanism of PP5, but the knowledge of how the deprotonation states of the two water molecules affect the binding of PP5 with its substrate is still lacking. To approach this problem, molecular dynamics simulations were performed to model the four possible deprotonation states. Through structural, dynamical and energetic analyses, the results demonstrate that the deprotonation states of the two water molecules affect the structure of the active site including the distance between the two Mn²⁺ ions and their coordination, impact the interaction energy of residues R275, R400 and H304 which directly interact with the substrate phosphoserine, and mediate the dynamics of helix αJ which is involved in regulation of the enzyme's activity. Furthermore, the deprotonation state that is preferable for PP5 binding of its substrate has been identified. These findings could provide new design strategy for PP5 inhibitor.     

A molecular dynamics study of the three-dimensional model of human synovial fluid phospholipase A2—transition state mimic complexes

Different modes of binding of transition state mimics: amide, phosphonate and difluoro ketone, to human synovial fluid phospholipase A₂ (HSF PLA₂) are studies by molecular dynamics simulations computed in solvent. The results are analysed in the light of primary binding sites. Hydrogen bonding interaction plays an important role for amino acids such as Gly32, Val30, and Glu55, apart from the well known active site residues viz Asp48, Gly25, Gly29, Gly31, His27, His47, Lys62, Phe23, Asn114 and Tyr112. In addition, the hydrogen bonding interaction between Sn-1 tetrahedral phosphonate group of amide and difluoro ketone inhibitors and crystallographic water molecules (H₂O 523, H₂O 524 and H₂O 401) seems to have a significant role. Many of the active site charged residues display considerable movement upon ligand binding. The structural effects of ligand binding were analyzed from RMS deviations of Cα in the resulting energy-minimized average structures of the receptor–ligand complexes. The values of the RMS deviations differ among the HSF PLA₂s, in a pattern that is not the same for the three complexes. This suggests that ligands with different pharmacological efficacies induce different types of conformational changes of the receptor. Our active-orientation model is, at least qualitatively, consistent with experimental data and should be useful for the rational design of more potent inhibitors.     

Interaction of human SRY protein with DNA: A molecular dynamics study

Molecular dynamics simulations have been conducted to study the interaction of human sex-determining region Y (hSRY) protein with DNA. For this purpose, simulations of the hSRY high mobility group (HMG) domain (hSRY-HMG) with and without its DNA target site, a DNA octamer, and the DNA octamer alone have been carried out, employing the NMR solution structure of hSRY-HMG–DNA complex as a starting model. Analyses of the simulation results demonstrated that the interaction between hSRY and DNA was hydrophobic, just a few hydrogen bonds and only one water molecule as hydrogen-bonding bridge were observed at the protein–DNA interface. These two hydrophobic cores in the hSRY-HMG domain were the physical basis of hSRY-HMG–DNA specific interaction. They not only maintained the stability of the complex, but also primarily caused the DNA deformation. The salt bridges formed between the positive-charged residues of hSRY and phosphate groups of DNA made the phosphate electroneutral, which was advantageous for the deformation of DNA and the formation of a stable complex. We predicted the structure of hSRY-HMG domain in the free state and found that both hSRY and DNA changed their conformations to achieve greater complementarity of geometries and properties during the binding process; that is, the protein increased the angle between its long and short arms to accommodate the DNA, and the DNA became bent severely to adapt to the protein, although the conformational change of DNA was more severe than that of the hSRY-HMG domain. The sequence specificity and the role of residue Met9 are also discussed. Proteins 31:417–433, 1998. © 1998 Wiley-Liss, Inc.     

Model-free methods of analyzing domain motions in proteins from simulation: A comparison of normal mode analysis and molecular dynamics simulation of lysozyme

Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations. For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by modes of motion external to the domains. To analyze the molecular dynamics trajectory, a principal component analysis tailored specifically to analyze interdomain motions is applied. A method based on the curl of the atomic displacements is described, which yields a sharp discrimination of domains, and which defines a unique interdomain screw-axis. Hinge axes are defined and classified as twist or closure axes depending on their direction. The methods have been tested on lysozyme. A remarkable correspondence was found between the first normal mode axis and the first principal mode axis, with both axes passing within 3 Å of the alpha-carbon atoms of residues 2, 39, and 56 of human lysozyme, and near the interdomain helix. The axes of the first modes are overwhelmingly closure axes. A lesser degree of correspondence is found for the second modes, but in both cases they are more twist axes than closure axes. Both analyses reveal that the interdomain connections allow only these two degrees of freedom, one more than provided by a pure mechanical hinge. Proteins 27:425–437, 1997. © 1997 Wiley-Liss, Inc.     

The stability of cylindrin β‐barrel amyloid oligomer models—A molecular dynamics study

Small‐soluble amyloid oligomers are believed to play a significant role in the pathology of amyloid diseases. Recently, the atomic structure of a toxic oligomer formed by an 11 residue and its tandem repeat was found to have an out‐off register antiparallel β‐strands in the shape of a β‐barrel. In the present article we investigate the effect of mutations in the hydrophobic cores on the structure and dynamic of the β‐barrels using all atom multiple molecular dynamics simulations with an explicit solvent. Extending previous experiments with molecular dynamics simulations we systematically test how stability and formation of cylindrin depends on the interplay between hydrophobicity and steric effects of the core residues. We find that strong hydrophobic interactions between geometrically fitting residues keep the strands (both in register and out‐off‐register interface) in close proximity, which in turn stabilizes the side‐chain and main‐chain hydrogen bonds, and the salt bridges on the outer surface along the weak out‐of‐register interface. Our simulations also indicate presence of water molecules in the hydrophobic interior of the cylindrin β‐barrel.Proteins 2013. © 2013 Wiley Periodicals, Inc.     

Drug‐binding energetics of human α‐1‐acid glycoprotein assessed by isothermal titration calorimetry and molecular docking simulations

This study utilizes sensitive, modern isothermal titration calorimetric methods to characterize the microscopic thermodynamic parameters that drive the binding of basic drugs to α‐1‐acid glycoprotein (AGP) and thereby rationalize the thermodynamic data in relation to docking models and crystallographic structures of the drug–AGP complexes. The binding of basic compounds from the tricyclic antidepressant series, together with miaserine, chlorpromazine, disopyramide and cimetidine, all displayed an exothermically driven binding interaction with AGP. The impact of protonation/deprotonation events, ionic strength, temperature and the individual selectivity of the A and F1*S AGP variants on drug‐binding thermodynamics was characterized. A correlation plot of the thermodynamic parameters for all of the test compounds revealed that an enthalpy–entropy compensation is in effect. The exothermic binding energetics of the test compounds were driven by a combination of favorable (negative) enthalpic (?Hº) and favorable (positive) entropic (?Sº) contributions to the Gibbs free energy (?Gº). Collectively, the data imply that the free energies that drive drug binding to AGP and its relationship to drug serum residency evolve from the complex interplay of enthalpic and entropic forces from interactions with explicit combinations of hydrophobic and polar side‐chain sub‐domains within the multi‐lobed AGP ligand binding cavity.Copyright © 2012 John Wiley & Sons, Ltd.     

The N‐terminal of annexin A1 as a secondary membrane binding site: A molecular dynamics study

Annexin A1 has been shown to cause membrane aggregation and fusion, yet the mechanism of these activities is not clearly understood. In this work, molecular dynamics simulations were performed on monomeric annexin A1 positioned between two negatively charged monolayers using AMBER's all atom force field to gain insight into the mechanism of fusion. Each phospolipid monolayer was made up of 180 DOPC molecules and 45 DOPG molecules to achieve a 4:1 ratio. The space between the two monolayers was explicitly solvated using TIP3P waters in a rectilinear box. The constructed setup contained up to 0.14 million atoms. Application of periodic boundary conditions to the simulation setup gave the desired effect of two continuous membrane bilayers. Nonbonded interactions were calculated between the N‐terminal residues and the bottom layer of phospholipids, which displayed a strong attraction of K26 and K29 to the lipid head‐groups. The side‐chains of these two residues were observed to orient themselves in close proximity (～3.5 Å) with the polar head‐groups of the phospholipids. Proteins 2014; 82:2936–2942. © 2014 Wiley Periodicals, Inc.     

A molecular dynamics study of Beta-Glucosidase B upon small substrate binding

Paenibacillus polymyxa β-glucosidase B (BglB), belongs to a GH family 1, is a monomeric enzyme that acts as an exo-β-glucosidase hydrolysing cellobiose and cellodextrins of higher degree of polymerization using retaining mechanism. A molecular dynamics (MD) simulation was performed at 300 K under periodic boundary condition for 5 ns using the complexes structure obtained from previous docking study, namely BglB-Beta-d-glucose and BglB-Cellobiose. From the root-mean-square deviation analysis, both enzyme complexes were reported to deviate from the initial structure in the early part of the simulation but it was stable afterwards. The root-mean-square fluctuation analysis revealed that the most flexible regions comprised of the residues from 26 to 29, 43 to 53, 272 to 276, 306 to 325 and 364 to 367. The radius of gyration analysis had shown the structure of BglB without substrate became more compact towards the end of the simulation compare to other two complexes. The residues His122 and Trp410 were observed to form stable hydrogen bond with occupancy higher than 10%. In conclusion, the behaviour of BglB enzyme towards the substrate binding was successfully explored via MD simulation approaches.