Thermodynamic and structural studies of carbohydrate binding by the agrin-G3 domain

Agrin is a key heparan sulfate proteoglycan involved in the development and maintenance of synaptic junctions between nerves and muscles. Agrin's important functions include clustering acetylcholine receptors on the postsynaptic membranes of muscles and binding to the muscle protein alpha-dystroglycan through its glycan chains. ITC and NMR were used to study the interactions of the C-terminal domain, agrin-G3, with carbohydrates implicated in agrin's functions. Sialic acid caps the glycan chains of alpha-dystroglycan and occurs as a posttranslational modification on the muscle-specific kinase component of the agrin receptor. We found that agrin-G3 binds sialic acid in a Ca2+-dependent manner. ITC data indicate that binding is exothermic and occurs with a 1:1 stoichiometry. NMR chemical shift changes map the sialic acid binding site to the loops that control the domain's acetylcholine receptor clustering activity. By contrast, the glycosaminoglycans heparin and heparan sulfate bind independently of Ca2+. Binding is endothermic, and the binding site spans about 12 saccharide units. The binding site for heparin occupies a similar location but is distinct from that for sialic acid. NMR translational diffusion experiments show that agrin-G3 binds heparin with a 2:1 stoichiometry. Comparisons between the muscle (B0) and neuronal (B8) isoforms of the agrin domain showed very similar Ca2+ and carbohydrate binding properties. Our work identifies agrin-G3 as a functional analogue of the concanavalin A-type lectins, highlights functional similarities between agrin and laminin G domains, and provides mechanistic clues about the roles of carbohydrates in agrin's functions.     

T-shaped arrangement of the recombinant agrin G3-IgG Fc protein

Agrin is a large heparin sulphate proteoglycan with multiple domains, which is located in the extracellular matrix. The C-terminal G3 domain of agrin is functionally one of the most important domains. It harbors an α-dystroglycan binding site and carries out acetylcholine receptor clustering activities. In the present study, we have fused the G3 domain of agrin to an IgG Fc domain to produce a G3-Fc fusion protein that we intend to use as a tool to investigate new binding partners of agrin. As a first step of the study, we have characterized the recombinant fusion protein using a multidisciplinary approach using dynamic light scattering, analytical ultracentrifugation and small angle X-ray scattering (SAXS). Interestingly, our SAXS analysis using the high-resolution structures of G3 and Fc domain as models indicates that the G3-Fc protein forms a T-shaped molecule with the G3 domains extruding perpendicularly from the Fc scaffold. To validate our models, we have used the program HYDROPRO to calculate the hydrodynamic properties of the solution models. The calculated values are in excellent agreement with those determined experimentally.     

Three-dimensional structure of soybean beta-amylase determined at 3.0 A resolution: preliminary chain tracing of the complex with alpha-cyclodextrin.

The three-dimensional structure of a complex of soybean beta-amylase [EC 3.2.1.2] with an inhibitor, alpha-cyclodextrin, has been determined at 3.0 A resolution by X-ray diffraction analysis. Preliminary chain tracing showed that the enzyme folded into large and small domains. The large domain has a (beta alpha)8 super-secondary structure, while the smaller one is formed from two long loops extending from the beta 3 and beta 4 strands of the (beta alpha)8 structure. The interface of the two domains together with shorter loops from the (beta alpha)8 structure form a deep cleft, in which alpha-cyclodextrin binds slightly away from the center. Two maltose molecules also bind in the cleft. One shares a binding site with alpha-cyclodextrin and the other is situated more deeply in the cleft.     

G protein-coupled receptor Kinase 2/G alpha q/11 interaction. A novel surface on a regulator of G protein signaling homology domain for binding G alpha subunits

G protein-coupled receptors (GPCRs) transduce cellular signals from hormones, neurotransmitters, light, and odorants by activating heterotrimeric guanine nucleotide-binding (G) proteins. For many GPCRs, short term regulation is initiated by agonist-dependent phosphorylation by GPCR kinases (GRKs), such as GRK2, resulting in G protein/receptor uncoupling. GRK2 also regulates signaling by binding G alpha(q/ll) and inhibiting G alpha(q) stimulation of the effector phospholipase C beta. The binding site for G alpha(q/ll) resides within the amino-terminal domain of GRK2, which is homologous to the regulator of G protein signaling (RGS) family of proteins. To map the Galpha(q/ll) binding site on GRK2, we carried out site-directed mutagenesis of the RGS homology (RH) domain and identified eight residues, which when mutated, alter binding to G alpha(q/ll). These mutations do not alter the ability of full-length GRK2 to phosphorylate rhodopsin, an activity that also requires the amino-terminal domain. Mutations causing G alpha(q/ll) binding defects impair recruitment to the plasma membrane by activated G alpha(q) and regulation of G alpha(q)-stimulated phospholipase C beta activity when introduced into full-length GRK2. Two different protein interaction sites have previously been identified on RH domains. The G alpha binding sites on RGS4 and RGS9, called the "A" site, is localized to the loops between helices alpha 3 and alpha 4, alpha 5 and alpha 6, and alpha 7 and alpha 8. The adenomatous polyposis coli (APC) binding site of axin involves residues on alpha helices 3, 4, and 5 (the "B" site) of its RH domain. We demonstrate that the G alpha(q/ll) binding site on the GRK2 RH domain is distinct from the "A" and "B" sites and maps primarily to the COOH terminus of its alpha 5 helix. We suggest that this novel protein interaction site on an RH domain be designated the "C" site.     

Functional glycan-free adhesion domain of human cell surface receptor CD58: design, production and NMR studies.

A general strategy is presented here for producing glycan-free forms of glycoproteins without loss of function by employing apolar-to-polar mutations of surface residues in functionally irrelevant epitopes. The success of this structure-based approach was demonstrated through the expression in Escherichia coli of a soluble 11 kDa adhesion domain extracted from the heavily glycosylated 55 kDa human CD58 ectodomain. The solution structure was subsequently determined and binding to its counter-receptor CD2 studied by NMR. This mutant adhesion domain is functional as determined by several experimental methods, and the size of its binding site has been probed by chemical shift perturbations in NMR titration experiments. The new structural information supports a 'hand-shake' model of CD2-CD58 interaction involving the GFCC'C" faces of both CD2 and CD58 adhesion domains. The region responsible for binding specificity is most likely localized on the C, C' and C" strands and the C-C' and C'-C" loops on CD58.     

Olfactory marker protein (OMP) exhibits a beta-clam fold in solution: implications for target peptide interaction and olfactory signal transduction

Olfactory marker protein (OMP) is a ubiquitous, cytoplasmic protein found in mature olfactory receptor neurons of all vertebrates. Electrophysiological and behavioral studies demonstrate that it is a modulator of the olfactory signal transduction pathway. Here, we demonstrate that the solution structure of OMP, as determined by NMR studies, is a single globular domain protein comprised of eight beta-strands forming two beta-sheets oriented orthogonally to one another, thus exhibiting a "beta-clam" or "beta-sandwich" fold: beta-sheet 1 is comprised of beta3-beta8-beta1-beta2 and beta-sheet 2 contains beta6-beta5-beta4-beta7. Insertions include two, long alpha-helices located on opposite sides of the beta-clam and three flexible loops. The juxtaposition of beta-strands beta6-beta5-beta4-beta7-beta2-beta1-beta8-beta3 forms a continuously curved surface and encloses one side of the beta-clam. The "cleft" formed by the two beta-sheets is opposite to the closed end of the beta-clam. Using a peptide titration series, we have identified this cleft as the binding surface for a peptide derived from the Bex1 protein. The highly conserved Omega-loop structure adjacent to the Bex1 peptide-binding surface found in OMP may be the site of additional OMP-protein interactions related to its role in modulating olfactory signal transduction. Thus, the interaction between the OMP and Bex1 proteins could facilitate the interaction between OMP and other components of the olfactory signaling pathway.     

Structure of lithocholic acid binding to the N-terminal 8-kDa domain of DNA polymerase beta

The purpose of this study was to investigate the molecular action of lithocholic acid (LCA), known as a selective inhibitor of DNA polymerase beta (pol beta). The 39-kDa pol beta was separated proteolytically into two fragments of the template-primer binding domain (8 kDa) and the catalytic domain (31 kDa). LCA bound tightly to the 8-kDa fragment but not to the 31-kDa fragment. We examined the structural interaction with the 8-kDa domain using LCA. On (1)H-(15)N HMQC NMR analysis of pol beta with LCA, the 8-kDa domain bound to LCA as a 1:1 complex with a dissociation constant (K(D)) of 1.56 mM. The chemical shifts were observed only in residues mainly in helix-3, helix-4, and the 79-87 turn of the same face. No significant shifts were observed for helix-1, helix-2, and other loops of the 8-kDa domain. This region was composed mainly of three amino acid residues (Lys60, Leu77, and Thr79) of pol beta on the LCA interaction interface. The inhibition mechanism and the structure-function relationship between pol beta and LCA is discussed.     

X-Ray structures of the universal translation initiation factor IF2/eIF5B: conformational changes on GDP and GTP binding

X-ray structures of the universal translation initiation factor IF2/eIF5B have been determined in three states: free enzyme, inactive IF2/eIF5B.GDP, and active IF2/eIF5B.GTP. The "chalice-shaped" enzyme is a GTPase that facilitates ribosomal subunit joining and Met-tRNA(i) binding to ribosomes in all three kingdoms of life. The conserved core of IF2/eIF5B consists of an N-terminal G domain (I) plus an EF-Tu-type beta barrel (II), followed by a novel alpha/beta/alpha-sandwich (III) connected via an alpha helix to a second EF-Tu-type beta barrel (IV). Structural comparisons reveal a molecular lever, which amplifies a modest conformational change in the Switch 2 region of the G domain induced by Mg(2+)/GTP binding over a distance of 90 A from the G domain active center to domain IV. Mechanisms of GTPase function and ribosome binding are discussed.     

Calcium plays a critical role in determining the acetylcholine receptor-clustering activities of alternatively spliced isoforms of Agrin

Neural agrin, an extracellular matrix protein secreted by motor neurons, plays a key role in clustering of nicotinic acetylcholine receptors (AChR) on postsynaptic membranes of the neuromuscular junction. The action of agrin is critically dependent on an eight-amino acid insert (z8 insert) in the third of three consecutive laminin-like globular (G3) domains near the C terminus of neural agrin. Alternatively spliced agrin isoforms in non-neural tissue including muscle lack the z8 insert and are biologically inactive. Extracellular calcium has been shown to be imperative for the AChR-clustering activity of neural agrin. It is unclear, however, whether calcium preferentially interacts with the neural isoform or whether it acts solely as an intracellular messenger that mediates agrin signaling. Here, we report the G3 domain of rat neural agrin (AgG3z8) expressed in Pichia pastoris promoted AChR clustering on surface of C2C12 myotubes in a calcium-dependent manner. Direct binding of calcium to AgG3z8 was demonstrated by trypsin digestion and thermal denaturation experiments. Moreover, calcium induced a significant change in the conformation of AgG3z8, and the effect was correlated with an enhanced binding affinity of the protein to muscle receptor. Mutation of calcium-binding residues in the G3 domain diminished the conformational change of neural agrin, reduced its binding affinity to muscle membrane, and inhibited AChR-clustering activity. Conversely, the G3 domain of muscle agrin (AgG3z0) displayed little structural change in the presence of calcium, bound poorly to muscle surface, and was inactive in AChR-clustering assays. We conclude that distinct interactions of the G3 domain with calcium determine the biological activities of alternatively spliced agrin isoforms during synapse formation.     

Sulfoquinovosylmonoacylglycerol inhibitory mode analysis of rat DNA polymerase beta

We have previously reported that sulfoquinovosylmonoacylglycerol (SQMG) is a potent inhibitor of mammalian DNA polymerases. DNA polymerase beta (pol beta) is one of the most important enzymes protecting the cell against DNA damage by base excision repair. In this study, we characterized the inhibitory action of SQMG against rat pol beta. SQMG competed with both the substrate and the template-primer for binding to pol beta. A gel mobility shift assay and a polymerase activity assay showed that SQMG competed with DNA for a binding site on the N-terminal 8-kDa domain of pol beta, subsequently inhibiting its catalytic activity. Fragments of SQMG such as sulfoquinovosylglycerol (SQG) and fatty acid (myristoleic acid, MA) weakly inhibited pol beta activity and the inhibitory effect of a mixture of SQG and MA was stronger than that of SQG or MA. To characterize this inhibition more precisely, we attempted to identify the interaction interface between SQMG and the 8-kDa domain by NMR chemical shift mapping. Firstly, we determined the binding site on a fragment of SQMG, the SQG moiety. We observed chemical shift changes primarily at two sites, the residues comprising the C-terminus of helix-1 and the N-terminus of helix-2, and residues in helix-4. Finally, based on our present results and our previously reported study of the interaction interface of fatty acids, we constructed two three-dimensional models of a complex between the 8-kDa domain and SQMG and evaluated them by the mutational analysis. The models show a SQMG interaction interface that is consistent with the data.     

Grb7 SH2 domain structure and interactions with a cyclic peptide inhibitor of cancer cell migration and proliferation

Background

Human growth factor receptor bound protein 7 (Grb7) is an adapter protein that mediates the coupling of tyrosine kinases with their downstream signaling pathways. Grb7 is frequently overexpressed in invasive and metastatic human cancers and is implicated in cancer progression via its interaction with the ErbB2 receptor and focal adhesion kinase (FAK) that play critical roles in cell proliferation and migration. It is thus a prime target for the development of novel anti-cancer therapies. Recently, an inhibitory peptide (G7-18NATE) has been developed which binds specifically to the Grb7 SH2 domain and is able to attenuate cancer cell proliferation and migration in various cancer cell lines.

Results

As a first step towards understanding how Grb7 may be inhibited by G7-18NATE, we solved the crystal structure of the Grb7 SH2 domain to 2.1 Å resolution. We describe the details of the peptide binding site underlying target specificity, as well as the dimer interface of Grb 7 SH2. Dimer formation of Grb7 was determined to be in the μM range using analytical ultracentrifugation for both full-length Grb7 and the SH2 domain alone, suggesting the SH2 domain forms the basis of a physiological dimer. ITC measurements of the interaction of the G7-18NATE peptide with the Grb7 SH2 domain revealed that it binds with a binding affinity of K_d = ~35.7 μM and NMR spectroscopy titration experiments revealed that peptide binding causes perturbations to both the ligand binding surface of the Grb7 SH2 domain as well as to the dimer interface, suggesting that dimerisation of Grb7 is impacted on by peptide binding.

Conclusion

Together the data allow us to propose a model of the Grb7 SH2 domain/G7-18NATE interaction and to rationalize the basis for the observed binding specificity and affinity. We propose that the current study will assist with the development of second generation Grb7 SH2 domain inhibitors, potentially leading to novel inhibitors of cancer cell migration and invasion.     

Mapping of binding sites for nidogens, fibulin-2, fibronectin and heparin to different IG modules of perlecan

Perlecan, a major basement membrane proteoglycan, has a complex modular structure designed for the binding of many cellular and extracellular ligands. Its domain IV, which consists of a tandem of immunoglobulin-like modules (IG2-IG15), is rich in such binding sites, which have been mapped to different modules obtained by recombinant production. Heparin/sulfatide binding was restricted to IG5 and shown to depend on four arginine residues that are close in space in beta strands B and E of the C-type IG fold. The nidogen-1 and nidogen-2 isoforms bind to IG3 with high affinity (K(d) approximately 10 nM). This interaction depends on the globular nidogen domain G2 and is crucial for the formation of ternary complexes with laminins. Two loops of IG3 located between beta strands B/C and F/G, which are spatially close, make a major contribution to binding. Fibronectin binding was localized to IG4-5 and fibulin-2 binds to IG2 and IG13-15 with different affinities. This implicates a complex cluster of heterotypic interaction sites apparently important for the supramolecular organization of perlecan in tissues.     

Dissection of the protein G B1 domain binding site for human IgG Fc fragment.

The contribution to the free energy of binding of each of the residues forming the binding site for a human IgG Fc fragment on the surface of the B1 domain of protein G was determined by alanine-scanning mutagenesis. The interface between these two proteins is atypical in that it is smaller than usual, polar in character, and involves two well-defined "knobs-into-holes" interactions. The bulk of the free energy of binding is contributed by three central residues, which make hydrogen bonds across the interface. Of these, the most critical interaction is formed by Glu27, which acts as a charged knob on the surface of the B1 domain, inserting into a polar hole on the Fc fragment. A single alanine mutation of this residue virtually abolishes stable complex formation. Formation of a stable interface between these two proteins is therefore dominated by a small, polar "hot spot."     

Loops within the CD11c I domain critical for specific recognition of fibrinogen

The I domains of CD11 are responsible for the binding of ligands and have a unique structure with 6-7 alpha helices and 6 beta sheets with interconnecting loops. To determine loops recognizing fibrinogen in CD11c I domain, five oligopeptides corresponding to CD11c loops were used to prevent fibrinogen binding to isolated CD11c I domain. The results of the inhibition experiment indicated that all of the loops except the one between E-beta sheet and 6-alpha helix were involved in the binding to fibrinogen. The peptide beta D alpha 5 and alpha 3 alpha 4 showed higher inhibitory activity than others, and the combination of four peptides blocked fibrinogen binding to the I domain completely. These peptides (beta A alpha 1, alpha 3 alpha 4, beta D alpha 5 and beta F alpha 7) could block THP-1 cell binding to fibrinogen coated surface as well. Alanine substitution of amino acids on the I domain such as Y249A and Q201A (which are on the loops beta D-alpha 5 and alpha 3-alpha 4 respectively) abolished fibrinogen binding, while mutation on the loop beta E-alpha 6 (Q273A) had no effect on fibrinogen binding. Taken together, the results from this study suggest that the loops on the top of CD11c I domain such as loop beta A-alpha 1, alpha 3-alpha 4, beta D-alpha 5 and beta F-alpha 7 are involved in fibrinogen binding, and two loops (alpha 3-alpha 4 and beta D-alpha 5) are more important than others for the recognition of fibrinogen.     

Crystal structure of the VHS and FYVE tandem domains of Hrs, a protein involved in membrane trafficking and signal transduction

We have determined the 2 A X-ray structure of the 219-residue N-terminal VHS and FYVE tandem domain unit of Drosophila Hrs. The unit assumes a pyramidal structure in which the much larger VHS domain (residues 1-153) forms a rectangular base and the FYVE domain occupies the apical end. The VHS domain is comprised of an unusual "superhelix" of eight alpha helices, and the FYVE domain is mainly built of loops, two double-stranded antiparallel sheets, and a helix stabilized by two tetrahedrally coordinated zinc atoms. The two-domain structure forms an exact 2-fold-related homodimer through antiparallel association of mainly FYVE domains. Dimerization creates two identical pockets designed for binding ligands with multiple negative charges such as citrate or phosphatidylinositol 3-phosphate.     

Interaction of agrin with laminin requires a coiled-coil conformation of the agrin-binding site within the laminin gamma1 chain

Coiled-coil domains are found in a wide variety of proteins, where they typically specify subunit oligomerization. Recently, we have demonstrated that agrin, a multidomain heparan sulfate proteoglycan with a crucial role in the development of the nerve-muscle synapse, binds to the three-stranded coiled-coil domain of laminin-1. The interaction with laminin mediates the integration of agrin into basement membranes. Here we characterize the binding site within the laminin-1 coiled coil in detail. Binding assays with individual laminin-1 full-length chains and fragments revealed that agrin specifically interacts with the gamma1 subunit of laminin-1, whereas no binding to alpha1 and beta1 chains was detected. By using recombinant gamma1 chain fragments, we mapped the binding site to a sequence of 20 residues. Furthermore, we demonstrate that a coiled-coil conformation of this binding site is required for its interaction with agrin. The finding that recombinant gamma1 fragments bound at least 10-fold less than native laminin-1 indicates that the structure of the three-stranded coiled-coil domain of laminin is required for high-affinity agrin binding. Interestingly, no binding to a chimeric gamma2 fragment was observed, indicating that the interaction of agrin with laminin is isoform specific.     

NMR reveals the absence of hydrogen bonding in adjacent UU and AG mismatches in an isolated internal loop from ribosomal RNA

NMR studies provide insights into structural features of internal loops. These insights can be combined with thermodynamic studies to generate models for predicting structure and energetics. The tandem mismatch internal loop, 5'GUGG3'(3'CUAC5'), has been studied by NMR. The NMR structure reveals an internal loop with no hydrogen bonding between the loop bases and with the G in the AG mismatch flipped out of the helix. The sequence of this internal loop is highly conserved in rRNA. The loop is located in the large ribosomal subunit and is part of a conserved 58-nt fragment that is the binding domain of ribosomal protein L11. Structural comparisons between variants of this internal loop in crystal structures of the 58-nt domain complexed with L11 protein and of the large ribosomal subunit (LSU) suggest that this thermodynamically destabilizing internal loop is partially preorganized for tertiary interactions and for binding L11. A model for predicting the base pairing and free energy of 2 x 2 nucleotide internal loops with a purine-purine mismatch next to a pyrimidine-pyrimidine mismatch is proposed on the basis of the present NMR structure and previously reported thermodynamics.     

A novel loop-loop recognition motif in the yeast ribosomal protein L30 autoregulatory RNA complex

The yeast Saccharomyces cerevisiae ribosomal protein L30 negatively autoregulates its production by binding to a helix-loop-helix structure formed in its pre-mRNA and its mRNA. A three-dimensional solution structure of the L30 protein in complex with its regulatory RNA has been solved using NMR spectroscopy. In the complex, the helix-loop-helix RNA adopts a sharply bent conformation at the internal loop region. Unusual RNA features include a purine stack, a reverse Hoogsteen base pair (G11anti-G56syn) and highly distorted backbones. The L30 protein is folded in a three-layer alpha/beta/alpha sandwich topology, and three loops at one end of the sandwich make base-specific contacts with the RNA internal loop. The protein-RNA binding interface is divided into two clusters, including hydrophobic and aromatic stacking interactions centering around G56, and base-specific hydrogen-bonding contacts to A57, G58 and G10-U60 wobble base pair. Both the protein and the RNA exhibit a partially induced fit for binding, where loops in the protein and the internal loop in the RNA become more ordered upon complex formation. The specific interactions formed between loops on L30 and the internal loop on the mRNA constitute a novel loop-loop recognition motif where an intimate RNA-protein interface is formed between regions on both molecules that lack regular secondary structure.     

Effect of pH and salt bridges on structural assembly: molecular structures of the monomer and intertwined dimer of the Eps8 SH3 domain

The SH3 domain of Eps8 was previously found to form an intertwined, domain-swapped dimer. We report here a monomeric structure of the EPS8 SH3 domain obtained from crystals grown at low pH, as well as an improved domain-swapped dimer structure at 1.8 A resolution. In the domain-swapped dimer the asymmetric unit contains two "hybrid-monomers." In the low pH form there are two independently folded SH3 molecules per asymmetric unit. The formation of intermolecular salt bridges is thought to be the reason for the formation of the dimer. On the basis of the monomer SH3 structure, it is argued that Eps8 SH3 should, in principle, bind to peptides containing a PxxP motif. Recently it was reported that Eps8 SH3 binds to a peptide with a PxxDY motif. Because the "SH3 fold" is conserved, alternate binding sites may be possible for the PxxDY motif to bind. The strand exchange or domain swap occurs at the n-src loops because the n-src loops are flexible. The thermal b-factors also indicate the flexible nature of n-src loops and a possible handle for domain swap initiation. Despite the loop swapping, the typical SH3 fold in both forms is conserved structurally. The interface of the acidic form of SH3 is stabilized by a tetragonal network of water molecules above hydrophobic residues. The intertwined dimer interface is stabilized by hydrophobic and aromatic stacking interactions in the core and by hydrophilic interactions on the surface.     

Mode analysis of a fatty acid molecule binding to the N-terminal 8-kDa domain of DNA polymerase beta. A 1:1 complex and binding surface.

We reported previously that long-chain fatty acids are potent inhibitors of mammalian DNA polymerase beta. At present, based on information available from the NMR structure of the N-terminal 8-kDa domain, we examined the structural interaction with the 8-kDa domain using two species, C(18)-linoleic acid (LA) or C(24)-nervonic acid (NA). In the 8-kDa domain with LA or NA, the structure that forms the interaction interface included helix-1, helix-2, helix-4, the three turns (residues 1-13, 48-51, and 79-87) and residues adjacent to an Omega-type loop connecting helix-1 and helix-2 of the same face. No significant shifts were observed for any of the residues on the opposite side of the 8-kDa domain. The NA interaction interface on the amino acid residues of the 8-kDa domain fragment was mostly the same as that of LA, except that the shifted cross-peaks of Leu-11 and Thr-79 were significantly changed between LA and NA. The 8-kDa domain bound to LA or NA as a 1:1 complex with a dissociation constant (K(D)) of 1.02 or 2.64 mM, respectively.