Lactam constraints provide insights into the receptor-bound conformation of secretin and stabilize a receptor antagonist

The natural ligands for family B G protein-coupled receptors are moderate-length linear peptides having diffuse pharmacophores. The amino-terminal regions of these ligands are critical for biological activity, with their amino-terminal truncation leading to production of orthosteric antagonists. The carboxyl-terminal regions of these peptides are thought to occupy a ligand-binding cleft within the disulfide-bonded amino-terminal domains of these receptors, with the peptides in amphipathic helical conformations. In this work, we have characterized the binding and activity of a series of 11 truncated and lactam-constrained secretin(5-27) analogues at the prototypic member of this family, the secretin receptor. One peptide in this series with lactam connecting residues 16 and 20 [c[E(16),K(20)][Y(10)]sec(5-27)] improved the binding affinity of its unconstrained parental peptide 22-fold while retaining the absence of endogenous biological activity and competitive antagonist characteristics. Homology modeling with molecular mechanics and molecular dynamics simulations established that this constrained peptide occupies the ligand-binding cleft in an orientation similar to that of natural full-length secretin and provided insights into why this peptide was more effective than other truncated conformationally constrained peptides in the series. This lactam bridge is believed to stabilize an extended α-helical conformation of this peptide while in solution and not to interfere with critical residue-residue approximations while docked to the receptor.     

Molecular basis of secretin docking to its intact receptor using multiple photolabile probes distributed throughout the pharmacophore

The molecular basis of ligand binding and activation of family B G protein-coupled receptors is not yet clear due to the lack of insight into the structure of intact receptors. Although NMR and crystal structures of amino-terminal domains of several family members support consistency in general structural motifs that include a peptide-binding cleft, there are variations in the details of docking of the carboxyl terminus of peptide ligands within this cleft, and there is no information about siting of the amino terminus of these peptides. There are also no empirical data to orient the receptor amino terminus relative to the core helical bundle domain. Here, we prepared a series of five new probes, incorporating photolabile moieties into positions 2, 15, 20, 24, and 25 of full agonist secretin analogues. Each bound specifically to the receptor and covalently labeled single distinct receptor residues. Peptide mapping of labeled wild-type and mutant receptors identified that the position 15, 20, and 25 probes labeled residues within the distal amino terminus of the receptor, whereas the position 24 probe labeled the amino terminus adjacent to TM1. Of note, the position 2 probe labeled a residue within the first extracellular loop of the receptor, a region not previously labeled, providing an important new constraint for docking the amino-terminal region of secretin to its receptor core. These additional experimentally derived constraints help to refine our understanding of the structure of the secretin-intact receptor complex and provide new insights into understanding the molecular mechanism for activation of family B G protein-coupled receptors.     

Structural analysis of pituitary adenylate cyclase-activating polypeptides bound to phospholipid membranes by magic angle spinning solid-state NMR

PACAP (pituitary adenylate cyclase-activating polypeptide) is a member of the VIP/secretin/glucagon family, which includes the ligands of class II G-protein coupled receptors. Since the recognition of PACAP by the receptor may involve the binding of PACAP to membranes, its membrane-bound structure should be important. We have carried out structural analysis of uniformly 13C,15N labeled PACAP27 and its C-terminal truncated form PACAP(1-21)NH2 (PACAP21) bound to membranes with high resolution solid-state NMR. Phosphatidylcholine bilayers and phosphatidylcholine/phosphatidylglycerol bilayers were used for PACAP27 and PACAP21, respectively. Most backbone signals were assigned for PACAP27 and PACAP21. TALOS analysis revealed that both peptides take on extended conformations on the membranes. Dilution of PACAP21 did not change the conformation of the major part. Selective polarization transfer experiment confirmed that PACAP27 is interacting with the membranes. It was concluded that the interaction of PACAP with the membrane surface causes their extended conformation. PACAP27 is reported to take an alpha-helical conformation in dodecylphosphocholine micelles and membrane-binding peptides usually take similar conformations in micelles and in membranes. Therefore, the property of PACAP27 changing its conformation in response to its environment is unique. Its conformational flexibility may be associated with its wide variety of functions.     

Structural analysis of pituitary adenylate cyclase-activating polypeptides bound to phospholipid membranes by magic angle spinning solid-state NMR

PACAP (pituitary adenylate cyclase-activating polypeptide) is a member of the VIP/secretin/glucagon family, which includes the ligands of class II G-protein coupled receptors. Since the recognition of PACAP by the receptor may involve the binding of PACAP to membranes, its membrane-bound structure should be important. We have carried out structural analysis of uniformly ¹³C,¹⁵N labeled PACAP27 and its C-terminal truncated form PACAP(1-21)NH₂ (PACAP21) bound to membranes with high resolution solid-state NMR. Phosphatidylcholine bilayers and phosphatidylcholine/phosphatidylglycerol bilayers were used for PACAP27 and PACAP21, respectively. Most backbone signals were assigned for PACAP27 and PACAP21. TALOS analysis revealed that both peptides take on extended conformations on the membranes. Dilution of PACAP21 did not change the conformation of the major part. Selective polarization transfer experiment confirmed that PACAP27 is interacting with the membranes. It was concluded that the interaction of PACAP with the membrane surface causes their extended conformation. PACAP27 is reported to take an α-helical conformation in dodecylphosphocholine micelles and membrane-binding peptides usually take similar conformations in micelles and in membranes. Therefore, the property of PACAP27 changing its conformation in response to its environment is unique. Its conformational flexibility may be associated with its wide variety of functions.     

Paired cysteine mutagenesis to establish the pattern of disulfide bonds in the functional intact secretin receptor

The amino-terminal domain of class B G protein-coupled receptors contains six conserved cysteine residues involved in structurally and functionally critical disulfide bonds. The mapping of these bonds has been unclear, with one pattern based on biochemical and NMR structural characterizations of refolded, nonglycosylated amino-terminal fragments, and another pattern derived from functional characterizations of intact receptors having paired cysteine mutations. In the present study, we determined the disulfide bonding pattern of the prototypic class B secretin receptor by applying the same paired cysteine mutagenesis approach and confirming the predicted bonding pattern with proteolytic cleavage of intact functional receptor. As expected, systematic mutation to serine of the six conserved cysteine residues within this region of the secretin receptor singly and in pairs resulted in loss of function of most constructs. Notable exceptions were single mutations of the 4th and 6th cysteine residues and paired mutations involving the 1st and 3rd, 2nd and 5th, and 4th and 6th conserved cysteines, with secretin eliciting statistically significant cAMP responses above basal levels of activation for each of these constructs. Immunofluorescence microscopy confirmed similar levels of plasma membrane expression for each of the mutated receptors. Furthermore, cyanogen bromide cleaved a series of wild type and mutant secretin receptors, yielding patterns that agreed with our paired cysteine mutagenesis results. In conclusion, these data suggest the same pattern of disulfide bonding as that predicted previously by NMR and thus support a consistent pattern of amino-terminal disulfide bonds in class B G protein-coupled receptors.     

Fluorescence resonance energy transfer analysis of secretin docking to its receptor: mapping distances between residues distributed throughout the ligand pharmacophore and distinct receptor residues

Full structural characterization of G protein-coupled receptors has been limited to rhodopsin, with its uniquely stable structure and ability to be crystallized. For other members of this important superfamily, direct structural insights have been limited to NMR structures of soluble domains. Two members of the Class II family have recently had the structures of their isolated amino-terminal regions solved by NMR, yet it remains unclear how that domain is aligned with the heptahelical transmembrane bundle domain of those receptors. Indeed, three distinct orientations have been suggested for different members of this family. In the current work, we have utilized fluorescence resonance energy transfer to establish the distances between four residues distributed throughout fully biologically active, high affinity analogues of secretin and distinct residues in each of four extracellular regions of the intact secretin receptor. These 16 distance constraints were utilized along with nine photoaffinity labeling spatial approximation constraints to study the three proposed orientations of the peptide-binding amino terminus and helical bundle domains of this receptor. In the best model, the carboxyl terminus of secretin was found to bind in a groove above the beta-hairpin region of the receptor amino terminus, with its amino-terminal end adjacent to the third extracellular loop and top of transmembrane segment VI. This refined model of the intact receptor was also fully consistent with the spatial approximation of the Trp(48)-Asp(49)-Asn(50) endogenous agonist segment with the third extracellular loop region that it has been shown to photolabel. This provides strong evidence for the orientation of peptide-binding and signaling domains of a prototypic Class II G protein-coupled receptor.     

Importance of each residue within secretin for receptor binding and biological activity

Secretin is a linear 27-residue peptide hormone that stimulates pancreatic and biliary ductular bicarbonate and water secretion by acting at its family B G protein-coupled receptor. While, like other family members, the carboxyl-terminal region of secretin is most important for high affinity binding and its amino-terminal region is most important for receptor selectivity and receptor activation, determinants for these activities are distributed throughout the entire length of this peptide. In this work, we have systematically investigated changing each residue within secretin to alanine and evaluating the impact on receptor binding and biological activity. The residues most critical for receptor binding were His1, Asp3, Gly4, Phe6, Thr7, Ser8, Leu10, Asp15, Leu19, and Leu23. The residues most critical for biological activity included His1, Gly4, Thr7, Ser8, Glu9, Leu10, Leu19, Leu22, and Leu23, with Asp3, Phe6, Ser11, Leu13, Asp15, Leu26, and Val27 also contributing. While the importance of residues in positions analogous to His1, Asp3, Phe6, Thr7, and Leu23 is conserved for several closely related members of this family, Leu19 is uniquely important for secretin. We, therefore, have further studied this residue by molecular modeling and molecular dynamics simulations. Indeed, the molecular dynamics simulations showed that mutation of Leu19 to alanine was destabilizing, with this effect greater than that observed for the analogous position in the other close family members. This could reflect reduced contact with the receptor or an increase in the solvent-accessible surface area of the hydrophobic residues in the carboxyl terminus of secretin as bound to its receptor.     

Identification of two pairs of spatially approximated residues within the carboxyl terminus of secretin and its receptor

The carboxyl-terminal domains of secretin family peptides have been shown to contain key determinants for high affinity binding to their receptors. In this work, we have examined the interaction between carboxyl-terminal residues within secretin and the prototypic secretin receptor. We previously utilized photoaffinity labeling to demonstrate spatial approximation between secretin residue 22 and the receptor domain that includes the first 30 residues of the amino terminus (Dong, M., Wang, Y., Pinon, D. I., Hadac, E. M., and Miller, L. J. (1999) J. Biol. Chem. 274, 903-909). Here, we further refined the site of labeling with the p-benzoyl-phenylalanine (Bpa(22)) probe to receptor residue Leu(17) using progressive cleavage of wild type and mutant secretin receptors (V13M and V16M) and sequence analysis. We also developed a new probe incorporating a photolabile Bpa at position 26 of secretin, closer to its carboxyl terminus. This analogue was also a potent agonist (EC(50) = 72 +/- 6 pm) and bound to the secretin receptor specifically and with high affinity (K(i) = 10.3 +/- 2.4 nm). It covalently labeled the secretin receptor at a single site saturably and specifically. This was localized to the segment between residues Gly(34) and Ala(41) using chemical and enzymatic cleavage of labeled wild type and A41M mutant receptor constructs and immunoprecipitation of epitope-tagged receptor fragments. Radiochemical sequencing identified the site of covalent attachment as residue Leu(36). These new insights, along with our recent report of contact between residue 6 within the amino-terminal half of secretin and this same amino-terminal region of this receptor (Dong, M., Wang, Y., Hadac, E. M., Pinon, D. I., Holicky, E. L., and Miller, L. J. (1999) J. Biol. Chem. 274, 19161-19167), support a key role for this region, making the molecular details of this interaction of major interest.     

Crystal structure of the PAC1R extracellular domain unifies a consensus fold for hormone recognition by class B G-protein coupled receptors

Pituitary adenylate cyclase activating polypeptide (PACAP) is a member of the PACAP/glucagon family of peptide hormones, which controls many physiological functions in the immune, nervous, endocrine, and muscular systems. It activates adenylate cyclase by binding to its receptor, PAC1R, a member of class B G-protein coupled receptors (GPCR). Crystal structures of a number of Class B GPCR extracellular domains (ECD) bound to their respective peptide hormones have revealed a consensus mechanism of hormone binding. However, the mechanism of how PACAP binds to its receptor remains controversial as an NMR structure of the PAC1R ECD/PACAP complex reveals a different topology of the ECD and a distinct mode of ligand recognition. Here we report a 1.9 Å crystal structure of the PAC1R ECD, which adopts the same fold as commonly observed for other members of Class B GPCR. Binding studies and cell-based assays with alanine-scanned peptides and mutated receptor support a model that PAC1R uses the same conserved fold of Class B GPCR ECD for PACAP binding, thus unifying the consensus mechanism of hormone binding for this family of receptors.     

Spatial approximation between two residues in the mid-region of secretin and the amino terminus of its receptor. Incorporation of seven sets of such constraints into a three-dimensional model of the agonist-bound secretin receptor

Photoaffinity labeling of receptors by bound agonists can provide important spatial constraints for molecular modeling of activated receptor complexes. Secretin is a 27-residue peptide hormone with a diffuse pharmacophoric domain that binds to the secretin receptor, a prototypic member of the Class B family of G protein-coupled receptors. In this work, we have developed, characterized, and applied two new photolabile probes for this receptor, with sites for covalent attachment in peptide positions 12 and 14, surrounding the previously most informative site of affinity labeling of this receptor. The [Tyr10,(BzBz)Lys12]rat secretin-27 probe covalently labeled receptor residue Val6, whereas the [Tyr10,(BzBz)Lys14]rat secretin-27 probe labeled receptor residue Pro38. When combined with previous photoaffinity labeling data, there are now seven independent sets of constraints distributed throughout the peptide and receptor amino-terminal domain that can be used together to generate a new molecular model of the ligand-occupied secretin receptor. The amino-terminal domain of this receptor presented a stable platform for peptide ligand interaction, with the amino terminus of the peptide hormone extended toward the transmembrane helix domain of the receptor. This provides clear insights into the molecular basis of natural ligand binding and supplies testable hypotheses regarding the molecular basis of activation of this receptor.     

Structural difference of vasoactive intestinal peptide in two distinct membrane-mimicking environments

Vasoactive intestinal peptide (VIP) is a 28-amino acid neuropeptide which belongs to a glucagon/secretin superfamily, the ligand of class II G protein-coupled receptors. Knowledge for the conformation of VIP bound to membrane is important because the receptor activation is initiated by membrane binding of VIP. We have previously observed that VIP-G (glycine-extended VIP) is unstructured in solution, as evidenced by the limited NMR chemical shift dispersion. In this study, we determined the three-dimensional structures of VIP-G in two distinct membrane-mimicking environments. Although these are basically similar structures composed of a disordered N-terminal region and a long α-helix, micelle-bound VIP-G has a curved α-helix. The side chains of residues Phe(6), Tyr(10), Leu(13), and Met(17) found at the concave face form a hydrophobic patch in the micelle-bound state. The structural differences in two distinct membrane-mimicking environments show that the micelle-bound VIP-G localized at the water-micelle boundary with these side chains toward micelle interior. In micelle-bound PACAP-38 (one of the glucagon/secretin superfamily peptide) structure, the identical hydrophobic residues form the micelle-binding interface. This result suggests that these residues play an important role for the membrane binding of VIP and PACAP.     

Analogs of pancreatic polypeptide and peptide YY with a locked PP-fold structure are biologically active

Pancreatic polypeptide (PP), peptide YY (PYY) and neuropeptide Y (NPY), members of the PP-fold family share a high degree of sequence homology. Nuclear magnetic resonance (NMR) and X-ray crystallography studies have shown these peptides can adopt a tightly organized tertiary structure called the PP-fold, which has long been assumed to be the active structure of this family of peptides. To date, however, no studies have been completed with PYY and PP which confirm if the PP-fold structure is important for their physiological actions. The aim of the study was to test if PYY and PP locked into the PP-fold maintained biological activity. Therefore, we designed and produced analogs of PP and PYY in a cyclic conformation with two cysteine amino acid substitutions at the N-terminus and at position 27. These were oxidized to form a cysteine disulfide bond locking the peptides into the PP-fold structure. Studies demonstrate that the cyclic analogs have both similar in vivo activity to their parent molecules, and affinity for the Y2 and Y4 receptors. Results suggest that the proposed PP and PYY-fold is likely to be their biologically active conformation.     

Contributions of domain structure and lipid interaction to the functionality of exchangeable human apolipoproteins

Exchangeable apolipoproteins function in lipid transport as structural components of lipoprotein particles, cofactors for enzymes and ligands for cell-surface receptors. Recent findings with apoA-I and apoE suggest that the tertiary structures of these two members of the human exchangeable apolipoprotein gene family are related. Characteristically, these proteins contain a series of proline-punctuated, 11- or 22-amino acid, amphipathic alpha-helical repeats that can adopt a helix bundle conformation in the lipid-free state. The amino- and carboxyl-terminal regions form separate domains with the latter being primarily responsible for lipid binding. Interaction with lipid induces changes in the conformation of the amino-terminal domain leading to alterations in function; for example, opening of the amino-terminal four-helix bundle in apolipoprotein E upon lipid binding is associated with enhanced receptor-binding activity. The concept of a two-domain structure for the larger exchangeable apolipoproteins is providing new molecular insights into how these apolipoproteins interact with lipids and other proteins, such as receptors. The ways in which structural changes induced by lipid interaction modulate the functionality of these apolipoproteins are reviewed.     

Conformation of a peptide ligand bound to its G-protein coupled receptor

Many peptide hormones elicit a wide array of physiological effects by binding to G-protein coupled receptors. We have determined the conformation of pituitary adenylate cyclase activating polypeptide, PACAP(1--21)NH(2), bound to a PACAP-specific receptor by NMR spectroscopy. Residues 3--7 form a unique beta-coil structure that is preceded by an N-terminal extended tail. This beta-coil creates a patch of hydrophobic residues that is important for receptor binding. In contrast, the C-terminal region (residues 8--21) forms an alpha-helix, similar to that in the micelle-bound PACAP. Thus, the conformational difference between PACAP in the receptor-bound and the micelle-bound states is limited to the N-terminal seven residues. This observation is consistent with the two-step ligand transportation model in which PACAP first binds to the membrane nonspecifically and then diffuses two-dimensionally in search of its receptor; a conformational change at the N-terminal region then allows specific interactions between the ligand and the receptor.     

Pituitary adenylate cyclase activating polypeptide regulates the basal production of nitric oxide in PC12 cells

Vasoactive intestinal peptide (VIP) and pituitary adenylate cyclase-activating polypeptide (PACAP), two members of the VIP/secretin/glucagon family, modulate neurotransmission via stimulation of protein kinases including cAMP-dependent protein kinase (PKA) and protein kinase C (PKC) in the central and peripheral nervous systems. They are reported to co-exist with nitric oxide synthases (NOSs) and other neuropeptides within the nervous system and peripheral tissues. In the present study, we investigated the neuronal role of these peptides in NO production in PC12 cells. We showed that PACAP decreased NO production in a dose-dependent manner, and the activators of protein kinase A and C also inhibited the NO production in PC12 cells. RT-PCR experiments demonstrated that PC12 cells constitutively express the mRNAs for neuronal NOS and the PACAP-specific (PAC1) receptor, and we concluded that PACAP plays an important role in the regulation of nNOS activity through PAC1 receptor in PC12 cells.     

Functional characterization of structural alterations in the sequence of the vasodilatory peptide maxadilan yields a pituitary adenylate cyclase-activating peptide type 1 receptor-specific antagonist.

Maxadilan is a vasodilatory peptide derived from sand flies that is an agonist at the pituitary adenylate cyclase-activating peptide (PACAP) type 1 receptor. Surprisingly, maxadilan does not share significant sequence homology with PACAP. To examine the relationship between structure and activity of maxadilan, several amino acid substitutions and deletions were made in the peptide. These peptides were examined in vitro for binding to crude membranes derived from rabbit brain, a tissue that expresses PACAP type 1 receptors; and induction of cAMP was determined in PC12 cells, a line that expresses these receptors. The peptides were examined in vivo for their ability to induce erythema in rabbit skin. Substitution of the individual cysteines at positions 1 and 5 or deletion of this ring structure had little effect on activity. Substitution of either cysteine at position 14 or 51 eliminated activity. Deletion of the 19 amino acids between positions 24 and 42 resulted in a peptide with binding, but no functional activity. The capacity of this deletion mutant to interact with COS cells transfected with the PACAP type 1 receptor revealed that this peptide was a specific antagonist to the PACAP type 1 receptor.     

Use of Cysteine Trapping to Map Spatial Approximations between Residues Contributing to the Helix N-capping Motif of Secretin and Distinct Residues within Each of the Extracellular Loops of Its Receptor

Amino-terminal regions of secretin-family peptides contain key determinants for biological activity and binding specificity, although the nature of interactions with receptors is unclear. A helix N-capping motif within this region has been postulated to directly contribute to agonist activity while also stabilizing formation of a helix extending toward the peptide carboxyl terminus and docking within the receptor amino terminus. We used cysteine trapping to systematically explore spatial approximations between cysteines replacing each residue in this motif of secretin (sec), Phe⁶, Thr⁷, and Leu¹⁰, and cysteines incorporated into the extracellular face of the receptor. Each peptide was a full agonist for cAMP, but had a lower binding affinity than natural hormone. These bound to COS cells expressing 61 receptor constructs incorporating cysteines in every position along each extracellular loop (ECL) and adjacent parts of transmembrane (TM) segments. Patterns of covalent labeling were distinct for each probe, with Cys⁶-sec labeling multiple residues in the carboxyl-terminal half of ECL2 and throughout ECL3, Cys⁷-sec predominantly labeling only single residues in the carboxyl-terminal end of ECL2 and the amino-terminal end of ECL3, and Cys¹⁰-sec not efficiently labeling any of these residues. These spatial constraints were used to refine our model of secretin bound to its receptor, now bringing ECL3 above the amino terminus of the ligand and revealing possible charge-charge interactions between this part of secretin and receptor residues in TM5, TM6, ECL2, and ECL3, which can orient and stabilize the peptide-receptor complex. This was validated by testing predicted approximations by mutagenesis and residue-residue complementation studies.     

Neurotransmitter and Immunomodulatory Actions of VIP and PACAP: Lessons from Knockout Mice

Vasoactive Intestinal Peptide (VIP) and Pituitary Adenylyl Cyclase Activating Peptide (PACAP) are two closely related neuropeptides in the secretin family. They are widely expressed in the central and peripheral nervous systems, where they are classically thought to act as neurotransmitters or neuromodulators. They interact with high affinity receptors to regulate numerous behaviors as well as gastrointestinal, endocrine, cardiopulmonary, reproductive and immune functions. The recent generation of mice that specifically lack or overexpress VIP, PACAP or their receptors has yielded much new knowledge and enabled investigators to better understand the biological roles of these peptides and their impact on health. In this review, we attempt to summarize the major findings, but focus in greatest detail on the circadian and immune functions.Australian Peptite Conference Issue.     

Agnathan VIP, PACAP and Their Receptors: Ancestral Origins of Today's Highly Diversified Forms

VIP and PACAP are pleiotropic peptides belonging to the secretin superfamily of brain-gut peptides and interact specifically with three receptors (VPAC(1), PAC(1) and VPAC(2)) from the class II B G protein-coupled receptor family. There is immense interest regarding their molecular evolution which is often described closely alongside gene and/or genome duplications. Despite the wide array of information available in various vertebrates and one invertebrate the tunicate, their evolutionary origins remain unresolved. Through searches of genome databases and molecular cloning techniques, the first lamprey VIP/PACAP ligands and VPAC receptors are identified from the Japanese lamprey. In addition, two VPAC receptors (VPACa/b) are identified from inshore hagfish and ligands predicted for sea lamprey. Phylogenetic analyses group these molecules into their respective PHI/VIP, PRP/PACAP and VPAC receptor families and show they resemble ancestral forms. Japanese lamprey VIP/PACAP peptides synthesized were tested with the hagfish VPAC receptors. hfVPACa transduces signal via both adenylyl cylase and phospholipase C pathways, whilst hfVPACb was only able to transduce through the calcium pathway. In contrast to the widespread distribution of VIP/PACAP ligands and receptors in many species, the agnathan PACAP and VPAC receptors were found almost exclusively in the brain. In situ hybridisation further showed their abundance throughout the brain. The range of VIP/PACAP ligands and receptors found are highly useful, providing a glimpse into the evolutionary events both at the structural and functional levels. Though representative of ancestral forms, the VIP/PACAP ligands in particular have retained high sequence conservation indicating the importance of their functions even early in vertebrate evolution. During these nascent stages, only two VPAC receptors are likely responsible for eliciting functions before evolving later into specific subtypes post-Agnatha. We also propose VIP and PACAP's first functions to predominate in the brain, evolving alongside the central nervous system, subsequently establishing peripheral functions.