TIFAB regulates the TIFA-TRAF6 signaling pathway involved in innate immunity by forming a heterodimer complex with TIFA.

Nuclear factor κB (NF-κB) is activated by various inflammatory and infectious molecules and is involved in immune responses. It has been elucidated that ADP-ß-D-manno-heptose (ADP-Hep), a metabolite in gram-negative bacteria, activates NF-κB through alpha-kinase 1 (ALPK1)-TIFA-TRAF6 signaling. ADP-Hep stimulates the kinase activity of ALPK1 for TIFA phosphorylation. Complex formation between phosphorylation-dependent TIFA oligomer and TRAF6 promotes the polyubiquitination of TRAF6 for NF-κB activation. TIFAB, a TIFA homolog lacking a phosphorylation site and a TRAF6 binding motif, is a negative regulator of TIFA-TRAF6 signaling and is implicated in myeloid diseases. TIFAB is indicated to regulate TIFA-TRAF6 signaling through interactions with TIFA and TRAF6; however, little is known about its biological function. We demonstrated that TIFAB forms a complex not with the TIFA dimer, an intrinsic form of TIFA involved in NF-κB activation, but with monomeric TIFA. The structural analysis of the TIFA/TIFAB complex and the biochemical and cell-based analyses showed that TIFAB forms a stable heterodimer with TIFA, inhibits TIFA dimer formation, and suppresses TIFA-TRAF6 signaling. The resultant TIFA/TIFAB complex is a "pseudo-TIFA dimer" lacking the phosphorylation site and TRAF6 binding motif in TIFAB and cannot form the orderly structure as proposed for the phosphorylated TIFA oligomer involved in NF-κB activation. This study elucidated the molecular and structural basis for the regulation of TIFA-TRAF6 signaling by TIFAB.

A protective multiple gene-deleted African swine fever virus genotype II, Georgia 2007/1, expressing a modified non-haemadsorbing CD2v protein.

African swine fever virus is a complex DNA virus that causes high fatality in pigs and wild boar and has a great socio-economic impact. An attenuated genotype II strain was constructed by replacing the gene for wildtype CD2v protein with versions in which single or double amino acid substitutions were introduced to reduce or abrogate the binding to red blood cells and reduce virus persistence in blood. The mutant CD2v proteins were expressed at similar levels to the wildtype protein on the surface of infected cells. Three recombinant viruses also had K145R, EP153R, and in one virus DP148R genes deleted. Following immunization of pigs, the virus with a single amino acid substitution in CD2v, Q96R, induced moderate levels of replication, and 100% protection against virulent ASFV. Two additional recombinant viruses had two amino acid substitutions in CD2v, Q96R, and K108D, and induced no binding to red blood cells in vitro. In immunized pigs, reduced levels of virus in blood and strong early ASFV-specific antibody and cellular responses were detected. After challenge low to moderate replication of challenge virus was observed. Reduced clinical signs post-challenge were observed in pigs immunized with the virus from which DP148R gene was deleted. Protection levels of 83-100% were maintained across a range of doses. Further experiments with virus GeorgiaΔDP148RΔK145RΔEP153R-CD2v_mutantQ96R/K108D showed low levels of virus dissemination in tissue and transient clinical signs at high doses. The results support further evaluation of GeorgiaΔDP148RΔK145RΔEP153R-CD2v_mutantQ96R/K108D as a vaccine candidate.

Protonation states of Asp residues in the human Nudix hydrolase MTH1 contribute to its broad substrate recognition.

Human MutT homolog 1 (MTH1), also known as Nudix-type motif 1 (NUDT1), hydrolyzes 8-oxo-dGTP and 2-oxo-dATP with broad substrate recognition and has attracted attention in anticancer therapeutics. Previous studies on MTH1 have proposed that the exchange of the protonation state between Asp119 and Asp120 is essential for the broad substrate recognition of MTH1. To understand the relationship between protonation states and substrate binding, we determined the crystal structures of MTH1 at pH 7.7-9.7. With increasing pH, MTH1 gradually loses its substrate-binding ability, indicating that Asp119 is deprotonated at pH 8.0-9.1 in 8-oxo-dGTP recognition and Asp120 is deprotonated at pH 8.6-9.7 in 2-oxo-dATP recognition. These results confirm that MTH1 recognizes 8-oxo-dGTP and 2-oxo-dATP by exchanging the protonation state between Asp119 and Asp120 with higher pKa .

Differences in CD80 and CD86 transendocytosis reveal CD86 as a key target for CTLA-4 immune regulation.

CD28 and CTLA-4 (CD152) play essential roles in regulating T cell immunity, balancing the activation and inhibition of T cell responses, respectively. Although both receptors share the same ligands, CD80 and CD86, the specific requirement for two distinct ligands remains obscure. In the present study, we demonstrate that, although CTLA-4 targets both CD80 and CD86 for destruction via transendocytosis, this process results in separate fates for CTLA-4 itself. In the presence of CD80, CTLA-4 remained ligand bound, and was ubiquitylated and trafficked via late endosomes and lysosomes. In contrast, in the presence of CD86, CTLA-4 detached in a pH-dependent manner and recycled back to the cell surface to permit further transendocytosis. Furthermore, we identified clinically relevant mutations that cause autoimmune disease, which selectively disrupted CD86 transendocytosis, by affecting either CTLA-4 recycling or CD86 binding. These observations provide a rationale for two distinct ligands and show that defects in CTLA-4-mediated transendocytosis of CD86 are associated with autoimmunity.

Structure of the mammalian adenine DNA glycosylase MUTYH: insights into the base excision repair pathway and cancer.

Mammalian MutY homologue (MUTYH) is an adenine DNA glycosylase that excises adenine inserted opposite 8-oxoguanine (8-oxoG). The inherited variations in human MUTYH gene are known to cause MUTYH-associated polyposis (MAP), which is associated with colorectal cancer. MUTYH is involved in base excision repair (BER) with proliferating cell nuclear antigen (PCNA) in DNA replication, which is unique and critical for effective mutation-avoidance. It is also reported that MUTYH has a Zn-binding motif in a unique interdomain connector (IDC) region, which interacts with Rad9-Rad1-Hus1 complex (9-1-1) in DNA damage response, and with apurinic/apyrimidinic endonuclease 1 (APE1) in BER. However, the structural basis for the BER pathway by MUTYH and its interacting proteins is unclear. Here, we determined the crystal structures of complexes between mouse MUTYH and DNA, and between the C-terminal domain of mouse MUTYH and human PCNA. The structures elucidated the repair mechanism for the A:8-oxoG mispair including DNA replication-coupled repair process involving MUTYH and PCNA. The Zn-binding motif was revealed to comprise one histidine and three cysteine residues. The IDC, including the Zn-binding motif, is exposed on the MUTYH surface, suggesting its interaction modes with 9-1-1 and APE1, respectively. The structure of MUTYH explains how MAP mutations perturb MUTYH function.

Structural analysis of TIFA: Insight into TIFA-dependent signal transduction in innate immunity.

TRAF-interacting protein with a forkhead-associated (FHA) domain (TIFA), originally identified as an adaptor protein of TRAF6, has recently been shown to be involved in innate immunity, induced by a pathogen-associated molecular pattern (PAMP). ADP-ß-D-manno-heptose, a newly identified PAMP, binds to alpha-kinase 1 (ALPK1) and activates its kinase activity to phosphorylate TIFA. Phosphorylation triggers TIFA oligomerisation and formation of a subsequent TIFA-TRAF6 oligomeric complex for ubiquitination of TRAF6, eventually leading to NF-κB activation. However, the structural basis of TIFA-dependent TRAF6 signalling, especially oligomer formation of the TIFA-TRAF6 complex remains unknown. In the present study, we determined the crystal structures of mouse TIFA and two TIFA mutants-Thr9 mutated to either Asp or Glu to mimic the phosphorylation state-to obtain the structural information for oligomer formation of the TIFA-TRAF6 complex. Crystal structures show the dimer formation of mouse TIFA to be similar to that of human TIFA, which was previously reported. This dimeric structure is consistent with the solution structure obtained from small angle X-ray scattering analysis. In addition to the structural analysis, we examined the molecular assembly of TIFA and the TIFA-TRAF6 complex by size-exclusion chromatography, and suggested a model for the TIFA-TRAF6 signalling complex.

A molecular and preclinical comparison of the PD-1-targeted T-cell checkpoint inhibitors nivolumab and pembrolizumab.

T-cell checkpoint inhibition has a profound impact on cancer care and the programmed cell death protein 1 (PD-1)-targeted antibodies nivolumab and pembrolizumab have been two of the lead molecules of this therapeutic revolution. Their clinical comparability is a highly relevant topic of discussion, but to a significant degree is a consequence of their molecular properties. Here we provide a molecular, preclinical, and early clinical comparison of the two antibodies, based on the available data and recent literature. We acknowledge the limitations of such comparisons, but suggest that based on the available data, differences in clinical trial outcomes between nivolumab and pembrolizumab are more likely drug-independent than drug-dependent.

Structural and Kinetic Studies of the Human Nudix Hydrolase MTH1 Reveal the Mechanism for Its Broad Substrate Specificity.

The human MutT homolog 1 (hMTH1, human NUDT1) hydrolyzes oxidatively damaged nucleoside triphosphates and is the main enzyme responsible for nucleotide sanitization. hMTH1 recently has received attention as an anticancer target because hMTH1 blockade leads to accumulation of oxidized nucleotides in the cell, resulting in mutations and death of cancer cells. Unlike Escherichia coli MutT, which shows high substrate specificity for 8-oxoguanine nucleotides, hMTH1 has broad substrate specificity for oxidized nucleotides, including 8-oxo-dGTP and 2-oxo-dATP. However, the reason for this broad substrate specificity remains unclear. Here, we determined crystal structures of hMTH1 in complex with 8-oxo-dGTP or 2-oxo-dATP at neutral pH. These structures based on high quality data showed that the base moieties of two substrates are located on the similar but not the same position in the substrate binding pocket and adopt a different hydrogen-bonding pattern, and both triphosphate moieties bind to the hMTH1 Nudix motif (i.e. the hydrolase motif) similarly and align for the hydrolysis reaction. We also performed kinetic assays on the substrate-binding Asp-120 mutants (D120N and D120A), and determined their crystal structures in complex with the substrates. Analyses of bond lengths with high-resolution X-ray data and the relationship between the structure and enzymatic activity revealed that hMTH1 recognizes the different oxidized nucleotides via an exchange of the protonation state at two neighboring aspartate residues (Asp-119 and Asp-120) in its substrate binding pocket. To our knowledge, this mechanism of broad substrate recognition by enzymes has not been reported previously and may have relevance for anticancer drug development strategies targeting hMTH1.

Novel CD200 homologues iSEC1 and iSEC2 are gastrointestinal secretory cell-specific ligands of inhibitory receptor CD200R.

CD200R is an inhibitory receptor expressed on myeloid cells and some lymphoid cells, and plays important roles in negatively regulating immune responses. CD200 is the only known ligand of CD200R and broadly distributed in a variety of cell types. Here we identified novel CD200 homologues, designated iSEC1 and iSEC2, that are expressed exclusively by secretory cell lineages in the gastrointestinal epithelium while authentic CD200 is expressed by none of epithelial cells including secretory cells. Both iSEC1 and iSEC2 could bind to CD200R but not other members of the CD200R family. Notably, CD200R expression was confined to intraepithelial lymphocytes (IELs) among cells in the gastrointestinal epithelium. Binding of iSEC1 to CD200R on IELs resulted in the suppression of cytokine production and cytolytic activity by activated IELs. Thus, iSEC1 is a previously unappreciated CD200R ligand with restricted expression in gastrointestinal secretory cells and may negatively regulate mucosal immune responses.

Autosomal dominant immune dysregulation syndrome in humans with CTLA4 mutations.

The protein cytotoxic T lymphocyte antigen-4 (CTLA-4) is an essential negative regulator of immune responses, and its loss causes fatal autoimmunity in mice. We studied a large family in which five individuals presented with a complex, autosomal dominant immune dysregulation syndrome characterized by hypogammaglobulinemia, recurrent infections and multiple autoimmune clinical features. We identified a heterozygous nonsense mutation in exon 1 of CTLA4. Screening of 71 unrelated patients with comparable clinical phenotypes identified five additional families (nine individuals) with previously undescribed splice site and missense mutations in CTLA4. Clinical penetrance was incomplete (eight adults of a total of 19 genetically proven CTLA4 mutation carriers were considered unaffected). However, CTLA-4 protein expression was decreased in regulatory T cells (Treg cells) in both patients and carriers with CTLA4 mutations. Whereas Treg cells were generally present at elevated numbers in these individuals, their suppressive function, CTLA-4 ligand binding and transendocytosis of CD80 were impaired. Mutations in CTLA4 were also associated with decreased circulating B cell numbers. Taken together, mutations in CTLA4 resulting in CTLA-4 haploinsufficiency or impaired ligand binding result in disrupted T and B cell homeostasis and a complex immune dysregulation syndrome.

Impact of antibodies against amyloidogenic transthyretin (ATTR) on phenotypes of patients with familial amyloidotic polyneuropathy (FAP) ATTR Valine30Methionine.

BACKGROUND: This study investigated whether a relationship exists between the presence of de novo antibodies and the clinical manifestations of familial amyloidotic polyneuropathy (FAP). METHODS: Serum samples were collected from 25 Japanese and 6 Swedish FAP amyloidogenic transthyretin (ATTR) Valine30Methionine (V30M) patients, 4 asymptomatic Japanese ATTR V30M gene carriers, and 24 Japanese healthy volunteers. Study methods included enzyme-linked immunosorbent assay (ELISA) and mass spectrometry. RESULTS: Three Japanese and 5 Swedish patients had significantly higher levels of antibodies against ATTR than did healthy volunteers and asymptomatic gene carriers (P<0.05). All 8 patients with higher antibody levels were late-onset cases. The ratio of wild-type TTR to ATTR V30M in serum from the high-antibody group was higher than that of the low-antibody group. ELISA results revealed two epitopes at positions 24-35 and 105-115 of ATTR V30M. We found a significant positive correlation between levels of the antibody at positions 24-35 and the age at FAP onset (r=0.751, P<0.05). An age-dependent increase in the occurrence of antibodies was observed in these patients with an epitope at positions 24-35. CONCLUSIONS: These findings may help explain the differences in early- and late-onset FAP and/or the progression of FAP.

Structure and interactions of the human programmed cell death 1 receptor.

PD-1, a receptor expressed by T cells, B cells, and monocytes, is a potent regulator of immune responses and a promising therapeutic target. The structure and interactions of human PD-1 are, however, incompletely characterized. We present the solution nuclear magnetic resonance (NMR)-based structure of the human PD-1 extracellular region and detailed analyses of its interactions with its ligands, PD-L1 and PD-L2. PD-1 has typical immunoglobulin superfamily topology but differs at the edge of the GFCC' sheet, which is flexible and completely lacks a C" strand. Changes in PD-1 backbone NMR signals induced by ligand binding suggest that, whereas binding is centered on the GFCC' sheet, PD-1 is engaged by its two ligands differently and in ways incompletely explained by crystal structures of mouse PD-1 · ligand complexes. The affinities of these interactions and that of PD-L1 with the costimulatory protein B7-1, measured using surface plasmon resonance, are significantly weaker than expected. The 3-4-fold greater affinity of PD-L2 versus PD-L1 for human PD-1 is principally due to the 3-fold smaller dissociation rate for PD-L2 binding. Isothermal titration calorimetry revealed that the PD-1/PD-L1 interaction is entropically driven, whereas PD-1/PD-L2 binding has a large enthalpic component. Mathematical simulations based on the biophysical data and quantitative expression data suggest an unexpectedly limited contribution of PD-L2 to PD-1 ligation during interactions of activated T cells with antigen-presenting cells. These findings provide a rigorous structural and biophysical framework for interpreting the important functions of PD-1 and reveal that potent inhibitory signaling can be initiated by weakly interacting receptors.

Crystallization and preliminary X-ray analysis of human MTH1 with a homogeneous N-terminus.

Human MTH1 (hMTH1) is an enzyme that hydrolyses several oxidized purine nucleoside triphosphates to their corresponding nucleoside monophosphates. Crystallographic studies have shown that the accurate mode of interaction between 8-oxoguanine and hMTH1 cannot be understood without determining the positions of the H atoms, as can be observed in neutron and/or ultrahigh-resolution X-ray diffraction studies. The hMTH1 protein prepared in the original expression system from Escherichia coli did not appear to be suitable for obtaining high-quality crystals because the hMTH1 protein had heterogeneous N-termini of Met1 and Gly2 that resulted from N-terminal Met excision by methionine aminopeptidase from the E. coli host. To obtain homogeneous hMTH1, the Gly at the second position was replaced by Lys. As a result, mutant hMTH1 protein [hMTH1(G2K)] with a homogeneous N-terminus could be prepared and high-quality crystals which diffracted to near 1.1 Šresolution using synchrotron radiation were produced. The new crystals belonged to space group P2(1)2(1)2(1), with unit-cell parameters a = 46.36, b = 47.58, c = 123.89 Å.

Mutants of lymphotoxin-α with augmented cytotoxic activity via TNFR1 for use in cancer therapy.

The cytokine lymphotoxin-α (LTα) is a promising candidate for use in cancer therapy. However, the instability of LTαin vivo and the insufficient levels of tumor necrosis factor receptor 1 (TNFR1)-mediated bioactivity of LTα limit its therapeutic potential. Here, we created LTα mutants with increased TNFR1-mediated bioactivity by using a phage display technique. We constructed a phage library displaying lysine-deficient structural variants of LTα with randomized amino acid residues. After affinity panning, we screened three clones of lysine-deficient LTα mutant, and identified a LTα mutant with TNFR1-mediated bioactivity that was 32 times that of the wild-type LTα (wtLTα). When compared with wtLTα, the selected clone showed augmented affinity to TNFR1 due to slow dissociation rather than rapid association. In contrast, the mutant showed only 4 times the TNFR2-mediated activity of wtLTα. In addition, the LTα mutant strongly and rapidly activated caspases that induce TNFR1-mediated cell death, whereas the mutant and wtLTα activated nuclear factor-kappa B to a similar extent. Our data suggest that the kinetics of LTα binding to TNFR1 play an important role in signal transduction patterns, and a TNFR1-selective LTα mutant with augmented bioactivity would be a superior candidate for cancer therapy.

Preparation, crystallization and preliminary X-ray diffraction studies of the glycosylated form of human interleukin-23.

Interleukin-23 (IL-23), a member of the IL-12 family, is a heterodimeric cytokine composed of p19 and p40 subunits. IL-23 plays crucial roles in the activation, proliferation and survival of IL-17-producing helper T cells which induce various autoimmune diseases. Human p19 and p40 subunits were cloned and coexpressed in N-acetylglucosaminyltransferase I-negative 293S cells, which produce high-mannose-type glycosylated proteins in order to diminish the heterogeneity of modified N-linked glycans. The glycosylated human IL-23 was purified and crystallized by the hanging-drop vapour-diffusion method. X-ray diffraction data were then collected to 2.6 Å resolution. The crystal belonged to space group P6(1) or P6(5), with unit-cell parameters a = b = 108.94, c = 83.79 Å, γ = 120°. Assuming that the crystal contains one molecule per asymmetric unit, the calculated Matthews coefficient was 2.69 Å(3) Da(-1), with a solvent content of 54.2%. The structure was determined by the molecular-replacement method, with an initial R factor of 52.6%. After subsequent rigid-body and positional refinement, the R(work) and R(free) values decreased to 31.4% and 38.7%, respectively.

Diverse substrate recognition and hydrolysis mechanisms of human NUDT5.

Human NUDT5 (hNUDT5) hydrolyzes various modified nucleoside diphosphates including 8-oxo-dGDP, 8-oxo-dADP and ADP-ribose (ADPR). However, the structural basis of the broad substrate specificity remains unknown. Here, we report the crystal structures of hNUDT5 complexed with 8-oxo-dGDP and 8-oxo-dADP. These structures reveal an unusually different substrate-binding mode. In particular, the positions of two phosphates (α and ß phosphates) of substrate in the 8-oxo-dGDP and 8-oxo-dADP complexes are completely inverted compared with those in the previously reported hNUDT5-ADPR complex structure. This result suggests that the nucleophilic substitution sites of the substrates involved in hydrolysis reactions differ despite the similarities in the chemical structures of the substrates and products. To clarify this hypothesis, we employed the isotope-labeling method and revealed that 8-oxo-dGDP is attacked by nucleophilic water at Pß, whereas ADPR is attacked at Pα. This observation reveals that the broad substrate specificity of hNUDT5 is achieved by a diversity of not only substrate recognition, but also hydrolysis mechanisms and leads to a novel aspect that enzymes do not always catalyze the reaction of substrates with similar chemical structures by using the chemically equivalent reaction site.

Rigid-body ligand recognition drives cytotoxic T-lymphocyte antigen 4 (CTLA-4) receptor triggering.

The inhibitory T-cell surface-expressed receptor, cytotoxic T lymphocyte-associated antigen-4 (CTLA-4), which belongs to the class of cell surface proteins phosphorylated by extrinsic tyrosine kinases that also includes antigen receptors, binds the related ligands, B7-1 and B7-2, expressed on antigen-presenting cells. Conformational changes are commonly invoked to explain ligand-induced "triggering" of this class of receptors. Crystal structures of ligand-bound CTLA-4 have been reported, but not the apo form, precluding analysis of the structural changes accompanying ligand binding. The 1.8-Å resolution structure of an apo human CTLA-4 homodimer emphasizes the shared evolutionary history of the CTLA-4/CD28 subgroup of the immunoglobulin superfamily and the antigen receptors. The ligand-bound and unbound forms of both CTLA-4 and B7-1 are remarkably similar, in marked contrast to B7-2, whose binding to CTLA-4 has elements of induced fit. Isothermal titration calorimetry reveals that ligand binding by CTLA-4 is enthalpically driven and accompanied by unfavorable entropic changes. The similarity of the thermodynamic parameters determined for the interactions of CTLA-4 with B7-1 and B7-2 suggests that the binding is not highly specific, but the conformational changes observed for B7-2 binding suggest some level of selectivity. The new structure establishes that rigid-body ligand interactions are capable of triggering CTLA-4 phosphorylation by extrinsic kinase(s).

The crystal structure of the green tea polyphenol (-)-epigallocatechin gallate-transthyretin complex reveals a novel binding site distinct from the thyroxine binding site.

Amyloid fibril formation is associated with protein misfolding disorders, including neurodegenerative diseases such as Alzheimer's, Parkinson's, and Huntington's diseases. Familial amyloid polyneuropathy (FAP) is a hereditary disease caused by a point mutation of the human plasma protein, transthyretin (TTR), which binds and transports thyroxine (T(4)). TTR variants contribute to the pathogenesis of amyloidosis by forming amyloid fibrils in the extracellular environment. A recent report showed that epigallocatechin 3-gallate (EGCG), the major polyphenol component of green tea, binds to TTR and suppresses TTR amyloid fibril formation. However, structural analysis of EGCG binding to TTR has not yet been conducted. Here we first investigated the crystal structure of the EGCG-V30M TTR complex and found novel binding sites distinct from the thyroxine binding site, suggesting that EGCG has a mode of action different from those of previous chemical compounds that were shown to bind and stabilize the TTR tetramer structure. Furthermore, EGCG induced the oligomerization and monomer suppression in the cellular system of clinically reported TTR variants. Taken together, these findings suggest the possibility that EGCG may be a candidate compound for FAP therapy.

Creation of lysine-deficient mutant lymphotoxin-alpha with receptor selectivity by using a phage display system.

The cytokine lymphotoxin-alpha (LT alpha) activates various biological functions through its three receptor subtypes, tumor necrosis factor receptor 1 (TNFR1), TNFR2 and herpes virus entry mediator (HVEM), but the relative contribution of each receptor to each function is unclear. Therefore it is important to create mutant LT alpha with receptor selectivity for optimized cancer therapy and the analysis of receptor function. Here, we attempted to create a lysine-deficient mutant LT alpha with TNFR1-selective bioactivity using a phage display technique. We obtained the TNFR1-selective mutant LT alpha R1selLT, which contained the mutations K19N, K28Q, K39S, K84Q, K89V, and K119H. Compared with wild-type LT alpha (wtLT alpha), R1selLT showed several-fold higher bioactivity via TNFR1 but 40-fold lower bioactivity via TNFR2. Kinetic association-dissociation parameters of R1selLT with TNFR2 were higher than those of wtLT alpha, whereas these parameters of R1selLT with TNFR1 were lower than those of wtLT alpha, suggesting that destabilization of the R1selLT-TNFR2 complex causes the decreased bioactivity of R1selLT on TNFR2. We also showed that the K84Q mutation contributed to the enhanced activity via TNFR1, and K39S lowered activity via TNFR2. R1selLT likely will be useful in cancer therapy and in analysis of the LT alpha structure-function relationship.