Studies on pituitary follitropin. V. Isolation of the subunits of the human hormone and reaction of the amino groups with acylating agents.

The alpha and beta subunits of human follitropin were isolated in a high state of purity. The tryptophan fluorescence of the native hormone and the isolated beta subunit are different. The N-terminus of the alpha and beta subunits was identified as valine and aspartic acid respectively. While recombination of the isolated alpha and beta subunits restores the electrophoretic mobility of the intact hormone, its receptor binding activity cannot be fully regenerated. Substitution of the human follitropin alpha by an ovine lutropin alpha subunit, to form a recombinant with the follitropin beta subunit, generates a complex with 2-3 receptor binding activity of the native human follitropin and the same activity as ovine follitropin. Acylation of the intact hormone does not disrupt the quaternary structure but leads to complete inactivation. Acylation studies with the subunits suggests the crucial role of the epsilon-amino groups of the alpha subunit in determining biological activity.     

Further characterization of the ovine lutropin alpha and beta subunits prepared by the salt precipitation method.

The subunits of ovine lutropin prepared by acid dissociation and salt precipitation were characterized by end group analysis, tryptic peptide mapping, SDS gel electrophoresis and biological activity. No evidence of internal peptide cleavage was found in the alpha subunit. The subunits possessed low activity. The alpha and beta subunits recombined effectively to generate a complex that had full receptor binding activity and in vitro biological activity. The recombinants of subunits prepared by countercurrent distribution showed only 50% activity in both assays. The salt precipitation method alpha subunit could be completely reduced and reoxidized in the absence of denaturants. The reoxidized alpha subunit combines with the native beta subunit generating full activity. However, this recombined hormone tends to lose activity with time, suggesting that the reoxidation may not fully restore the native structur of the reduced alpha subunit. The native lutropin alpha subunit effectively combined with follitropin beta subunit generating complete follitropin activity.     

Porcine follitropin. Isolation and characterization of the native hormone and its alpha and beta subunits

The properties of porcine follitropin and its subunits which have not yet been characterized are presented. The porcine follitropin obtained has a biological potency of 81 times the National Institutes of Health Porcine Follitropin P-1 preparation. Its contamination by lutropin and thyrotropin amounted to 1 and 0.5 percent by weight respectively, as measured by radioimmunoassay. The alpha and beta subunits of porcine follitropin were obtained by incubation in an acidic urea solution followed by anion exchange chromatography. The amino acid composition of porcine follitropin alpha subunit was found to be identical to that of alpha chain of porcine lutropin and thyrotropin. These porcine alpha chains differ, nevertheless, markedly in their carbohydrate composition particularly with respect to their mannose and galactose contents. The amino-terminal residue of the follitropin alpha subunit is threonyl. The carboxy-terminal end of the alpha chain is of variable length. Cysteyl residue was detected at the aminoterminal end of the follitropin beta chain with glutamic acid at its carboxy-terminal end. Cross-contamination of the alpha and beta subunit preparations was measured by specific radioimmunoassay and amounted to 0.5 and 0.1 percent by weight respectively.     

Studies on pituitary follitropin. II. Isolation and characterization of the subunits of the ovine hormone.

The α and β subunits of highly potent ovine follitropin have been isolated by dissociation in 8 m urea, pH 7.5, and chromatography on DEAE-Sephadex A25. The isolated subunits display microheterogeneity on polyacrylamide gel electrophoresis and have very low activity in follitropin-specific radioreceptor and radioimmunoassays. The tryptophan fluorescence spectra of native follitropin and the isolated β subunit are different. The recombinant of follitropin α + β subunit had the same activity as the native hormone in the radioimmunoassay, but its activity in the radioreceptor and in vivo bioassay was about 65% of the intact hormone. Substitution of the follitropin α by ovine lutropin α subunit (prepared by a method not involving urea) to form the recombinant restored full activity in all the three assays investigated. The formation of recombined hormone proceeds at a rapid rate and is almost complete by 6 h. The α and β subunits of ovine follitropin differ from each other in amino acid composition. No significant differences were apparent in their carbohydrate composition. The amino acid composition of the ovine follitropin α and lutropin α subunits are very similar. The oxidized α subunit has phenylalanine at its NH₂-terminus while aspartic acid is present at this position in the oxidized β subunit.     

Bovine follitropin. Isolation and characterization of the native hormone and its alpha and beta subunits

1) A reproducible procedure was developed for the purification of bovine follitropin. 2) The method involved ammonium sulfate precipitation, ion exchange and adsorption chromatography, concanacaline-A-Sepharose chromatography and gel filtration. 3) A specific radioligand receptor assay was used to monitor each chromatographical step. 4) The potency of highly purified bovine follitropin as measured by Steelman and Pohley bioassay was 62 times the NIH-FSH-B1 standard preparation. 5) Contaminations of bovine follitropin by other glycoprotein hormones such as thyrotropin and lutropin amounted to 3 and 0.45 per cent by weight respectively as measured by specific radioimmunoassays and radioligand receptor assays. 6) The subunits alpha and beta of bovine follitropin were obtained by incubation in acidic urea, the chains being then separated by anion exchange chromatography. The subunits were subjitted to complete characterization. The amino-terminal residue of the alpha subunit is phenylalanine while a half cystine residue was found at the aminoterminal end of the beta chain. 8) Cross-contamination of the alpha and beta subunit preparations was measured by specific radioimmunoassays and amounted to 0.02 and 0.1 per cent by weight respectively.     

Physicochemical and biological characterizations of pregnant mare serum gonadotropin and its subunits.

Pregnant mare serum gonadotropin and its subunits have been further characterized. Ultracentrifugation of the gonadotropin at pH 1.3 and 11.5 showed little evidence of dissociation compared to pH 8.2. Highly purified subunits are obtained by urea dissociation and ion-exchange chromatography followed by gel-filtration. Circular dichroism spectra of the gonadotropin and its subunits are much like those of ovine lutropin and its subunits in that there is little evidence for secondary structure and one or more tyrosine residues are inaccessible in the intact gonadotropin compared to the subunits. The alpha-subunit possesses almost 3 times as much total carbohydrate as the beta-subunit; the individual sugar composition of each was determined as well as the amino acid composition. The alpha-subunit begins with the sequence NH2-Phe-Pro (Gly or Pro) ... and terminates with isoleucine. The beta-subunit has the sequence NH2-Ser-Pro-Gly ...; no C-terminal residue is detectable by either carboxypeptidase or hydrazinolysis. Biological studies show the gonadotropin to be active in assays specific for both lutropin and follitropin. Precipitin test in agar with rabbit antiserum against the gonadotropin show that the beta subunit cross-reacts whereas the alpha subunit does not.     

Physicochemical and biological characterizations of pregnant mare serum gonadotropin and its subunits

Pregnant mare serum gonadotropin and its subunits have been further characterized. Ultracentrifugation of the gonadotropin at pH 1.3 and 11.5 showed little evidence of dissociation compared to pH 8.2. Highly purified subunits are obtained by urea dissociation and ion-exchange chromatography followed by gel-filtration. Circular dichroism spectra of the gonadotropin and its subunits are much like those of ovine lutropin and its subunits in that there is little evidence for secondary structure and one or more tyrosine residues are inaccessible in the intact gonadotropin compared to the subunits. The α-subunit possesses almost 3 times as much total carbohydrate as the β-subunit; the individual sugar composition of each was determined as well as the amino acid composition. The α-subunit begins with the sequence NH₂-Phe-Pro (Gly or Pro) … and terminates with isoleucine. The β-subunit has the sequence NH₂-Ser-Pro-Gly …; no C-terminal residue is detectable by either carboxypeptidase or hydrazinolysis. Biological studies show the gonadotropin to be active in assays specific for both lutropin and follitropin. Precipitin test in agar with rabbit antiserum against the gonadotropin show that the beta subunit cross-reacts whereas the alpha subunit does not.     

Synthesis of multi-subunit domain gonadotropin complexes: a model for alpha/beta heterodimer formation

The human glycoprotein hormones chorionic gonadotropin (CG), thyrotropin (TSH), lutropin (LH), and follitropin (FSH) are heterodimers, composed of a common alpha subunit assembled to a hormone-specific beta subunit. The subunits combine noncovalently early in the secretory pathway and exist as heterodimers, but not as multimers. Little information is available regarding the steps associated with the assembly reaction. It is unclear if the initial alpha beta engagement results either in the formation of only mature heterodimer or if the nascent complex is reversible and can undergo an exchange of subunits or combine transiently with an additional subunit. This is relevant for the case of LH and FSH, because both are synthesized in the same cell (i.e., pituitary gonadotrophs) and several of the alpha subunit sequences required for association with either the LH beta or FSH beta subunits are different. Such features could favor the generation of short-lived, multi-subunit forms prior to completion of assembly. Previously, we showed that the CG beta or FSH beta subunit genes can be genetically fused to the alpha gene to produce biologically active single chains, CG beta alpha and F beta alpha, respectively. Studies using monoclonal antibodies sensitive to the conformation of the hCG subunits suggested that in contrast to the highly compact heterodimer, the interactions between the beta and alpha domains in the single chain are in a more relaxed configuration. That the tethered domains do not interact tightly predicts that they could combine with an additional subunit to form triple domain complexes. We tested this point by cotransfecting CHO cells with the genes encoding F beta alpha and the CG beta subunit or the CG beta alpha and FSH beta monomer. The CG beta subunit combined noncovalently with F beta alpha to form a F beta alpha/CG beta complex. Ternary complex formation was not restricted to a specific set of single chain/monomeric subunit, because a CG beta alpha/FSH beta complex was also detected implying that triple domain intermediates could be transiently generated along the secretory pathway. Monoclonal antibodies specific for the CG heterodimer recognized the F beta alpha/CG beta complex, which suggests that the epitopes unique for dimeric CG were established. In addition, media containing F beta alpha/CG beta displayed high-affinity binding to both CG and FSH receptors. The presence of CG activity is presumptive for the existence of a functional F beta alpha/CG beta complex, because neither F beta alpha nor the uncombined CG beta subunit binds to CG receptor. These data show that the alpha subunit of the tether, although covalently linked to the FSH beta domain, can functionally interact with a different beta subunit implying that the contacts in the nascent alpha beta dimer are reversible. The formation of a functional single chain/subunit complex was not restricted to the FSH single chain/CG beta subunit since CG single chain interacts with the monomeric FSH beta subunit and exhibits FSH activity. The presence of the triple domain configuration does not abolish bioactivity, suggesting that although the gonadotropins are heterodimers, the cognate receptor is capable of recognizing a larger ligand composed of three subunit domains.     

Rabbit lutropin: preparation, characterization of the hormone, its subunits and radioimmunoassay.

The purification of rabbit lutropin is described. A product with a potency of 1.53 X NIH-LH-Sl was obtained as assayed by the ovarian ascorbic acid depletion assay. In a homologous radioimmunoassay, which is described, rabbit lutropin has a potency 4.83 X NIH-LH-Sl. In a radioligand assay, utilizing labeled ovine lutropin as the trace, the relative potency was 0.47 X NIH-LH-Sl measured by 50% inhibition comparison since rabbit lutropin response in this system did not parallel ovine lutropin. A counter-current distribution procedure for separation of rabbit lutropin subunits is described. Amino acid composition of the isolated subunits and intact rabbit lutropin was determined. The carbohydrate composition of the latter is presented; only amino sugar determinations are available for the subunits. The NH2-terminal amino acids are phenylalanine (alpha subunit) and alanine (beta subunit). Preliminary data on COOH-terminal amino acids are provided.     

Reaction of tetranitromethane with lutropin, oxytocin, and vasopressin.

Tetranitromethane reaction with intact ovine lutropin and its isolated subunits was studied using spectrophotometric measurements, amino acid analysis, and isolation of tyrosyl peptides. Tyrosyl residues in the beta subunit (beta37, beta59) did not react with tetranitromethane in the intact hormone, but were nitrated in the isolated subunit. The sequence and extent of reaction of tetranitromethane with the tyrosyl residues in the alpha subunit was alpha21 = alpha92 = alpha93 (in intact hormone or isolated subunit) greater than alpha 41 (reacted in isolated subunit only) greater than alpha 30 (reacted in isolated subunit in 8 M urea only). Polymerization was observed as a side reaction in agreement with previous studies. The degree of polymerization appeared to be related to both primary sequence and tertiary structure, and for lutropin had the relation: alpha subunit (93% polymerized) greater than intact hormone greater than beta subunit (less than 40%). Polymerization observed with vasopressin was significantly greater than with oxytocin; for these peptides the tyrosine residues in the monomeric product were converted to 3-nitrotyrosine. Neither 3-nitrotyrosine nor tyrosine was detected in the polymerized by-products. In the tetranitromethane reaction with intact ovine lutropin, other reaction products charcterized by absorption spectra were found. Peptides isolated from these products lacked the characteristic 428 nm abosrption maxima of 3-nitrotyrosyl peptides and showed instead absorption in the 310 to 350 nm region. Similar products from tetranitromethane reactions with di- and tripeptides containing tyrosine have been observed previously (Boyd, N.D., and Smith, D.B. (1971) Can. J. Biochem, 49, 154-161), but they have not been studied in proteins. A possible relationship to the polymerization side reaction is suggested.     

In vitro activation of glycoprotein hormones. Hybridization of subunits from thyrotropin, lutropin and human choriogonadotropin.

In vitro assembly of thyrotropin alpha and beta subunits led to an increase in content of alpha helix and beta sheet very similar to that found for gonadotropins. This association-dependent active folding involved the burying of three tyrosine residues tentatively assigned to Tyr alpha 41, Tyr beta 37 and Tyr beta 59 and common to all studied glycoprotein hormones. In vitro hybridizations between alpha and beta subunits of various hormones (thyrotropin, lutropin and choriogonadotropin) from different species (ovine, bovine and human) triggered the same molecular events as assembly of homologous subunits: the burying of three tyrosine residues and the increase of periodic structure of the folding. These changes are slow, time-dependent processes. Rates and yields of hybrid formation measured by sedimentation analysis and difference spectroscopy of tyrosines are identical, within experimental error, with the rates and yields measured by the recovery of the biological activity either the stimulation of chick thyroids for thyrotropin-beta hybrids or binding to porcine testis receptors for gonadotropin-beta hybrids. Whatever the origin of the alpha subunit, the thyrotropin-beta hybrids were not able to bind to testis receptors although active on chick thyroids. Rates and yields of hybrid formation essentially depended on the origin of the beta subunit. All the hybrids could be dissociated at acid pH with rates similar to those of native hormone. The extension to thyrotropin and various hybrids of the structural features of the in vitro assembly already recognized for gonadotropins strengthens the hypothesis that one deals with a basic activation process which also occurs in vivo after the synthesis of the subunits.     

Origin of the mutual activation of the alpha and beta 2 subunits in the alpha 2 beta 2 complex of tryptophan synthase. Effect of alanine or glycine substitutions at proline residues in the alpha subunit.

To understand how the alpha and beta 2 subunits of tryptophan synthase from Escherichia coli interact to form an alpha 2 beta 2 complex and undergo mutual activation, we have investigated alpha subunits with single amino acid replacements at conserved proline residues. Although the activities of alpha 2 beta 2 complexes that contain wild type alpha subunit or alpha subunits substituted at positions 28, 62, 96, and 207 are similar, the activities of alpha 2 beta 2 complexes that contain alpha subunits substituted at positions 57 and 132 are remarkably altered. Whereas the latter enzymes have greatly reduced activities in the individual half-reactions, they have considerably higher activities in the overall reaction. These remarkable activity results are explained by a decrease in the affinity of these mutant alpha subunits for the beta 2 subunit and by an increase in the affinity in the combined presence of ligands of both the alpha subunit and the beta 2 subunit. Isothermal calorimetric titrations of wild type beta 2 subunit with wild type alpha subunit and a mutant alpha subunit containing a substitution of glycine for proline at position 132 show that both the affinity and the exothermic association enthalpy are greatly reduced in the mutant alpha subunit although the stoichiometry of association is unchanged. The affinity of the mutant alpha subunit for the beta 2 subunits is greatly increased in the presence of an alpha subunit ligand, alpha-glycerol phosphate. We conclude that proline 132 plays a critical role in subunit interaction and in mutual subunit activation.     

Preparation of lutropin with acetyl or acetimidinyl substituents on the amino groups of the beta-subunit.

The free amino groups in ovine lutropin beta subunit were acylated with acetic anhydride and methyl acetimidinate-HCl to produce the corresponding acetyl and acetimidinyl ovine lutropin beta derivative. These two derivatives recombined with ovine lutropin alpha as well as native ovine lutropin beta, but produced lutropin derivatives which were 33-50% less active than the ovine lutropin alpha + ovine lutropin beta in biological assays.     

Molecular determinants of glycine receptor subunit assembly.

The inhibitory glycine receptor (GlyR) is a pentameric transmembrane protein composed of homologous alpha and beta subunits. Single expression of alpha subunits generates functional homo-oligomeric GlyRs, whereas the beta subunit requires a co-expressed alpha subunit to assemble into hetero-oligomeric channels of invariant stoichiometry (alpha(3)beta(2)). Here, we identified eight amino acid residues within the N-terminal region of the alpha1 subunit that are required for the formation of homo-oligomeric GlyR channels. We show that oligomerization and N-glycosylation of the alpha1 subunit are required for transit from the endoplasmic reticulum to the Golgi apparatus and later compartments, and that addition of simple carbohydrate side chains occurs prior to GlyR subunit assembly. Our data are consistent with both intersubunit surface and conformational differences determining the different assembly behaviour of GlyR alpha and beta subunits.     

The voltage-sensitive sodium channel from rabbit skeletal muscle. Chemical characterization of subunits

The alpha and beta subunits of the rabbit skeletal muscle sodium channel have been separated and isolated preparatively under denaturing conditions. In this sodium channel, the beta subunit is not linked covalently to the alpha subunit. The isolated subunits have been subjected to amino acid and carbohydrate analysis. Both subunits are heavily glycosylated (alpha = 26.5%, beta = 29.7% carbohydrate by weight) with N-acetylneuraminic acid and N-acetylhexosamines representing the predominant monosaccharides in each. Enzymatic deglycosylation with neuraminidase and endoglycosidase F yielded single core peptides of approximately 209 kDa for the alpha subunit and 26.5 kDa for the beta subunit. Based on the known carbohydrate composition, the molecular masses for the glycosylated subunits are, therefore, 285 and 37.5 kDa for alpha and beta, respectively. Using the isolated subunits, we calibrated our protein-labeling system on sodium dodecyl sulfate-polyacrylamide gel electrophoresis and determined the subunit stoichiometry for the rabbit skeletal muscle channel; in the native preparation, the molar ratio of alpha:beta is 1 : 1.     

Overexpression and purification of the separate tryptophan synthase alpha and beta subunits from Salmonella typhimurium.

To obtain high levels of expression of the free alpha and beta subunits of tryptophan synthase from Salmonella typhimurium, we have used two plasmids (pStrpA and pStrpB) that carry the genes encoding the alpha and beta subunits, respectively. The expression of each plasmid in Escherichia coli CB149 results in overproduction of each subunit. We also report new and efficient methods for purifying the individual alpha and beta subunits. Microcrystals of the beta subunit are obtained by addition of polyethylene glycol 8000 and spermine to crude bacterial extracts. This crystallization procedure is similar to methods used previously to grow crystals of the S. typhimurium tryptophan synthase alpha 2 beta 2 complex for X-ray crystallography and to purify this complex by crystallization from bacterial extracts. The results suggest that purification by crystallization may be useful for other overexpressed enzymes and multienzymes complexes. Purification of the alpha subunit utilizes ammonium sulfate fractionation, chromatography on diethylaminoethyl-Sephacel, and high-performance liquid chromatography on a Mono Q column. The purified alpha and beta subunits are more than 95% pure by the criterion of sodium dodecyl sulfate gel electrophoresis. The procedures developed can be applied to the expression and purification of mutant forms of the separate alpha and beta subunits. The purified alpha and beta subunits provide useful materials for studies of subunit association and for investigations of other properties of the separate subunits.     

Subunit topography of RNA polymerase from Escherichia coli. A cross-linking study with bifunctional reagents.

The quaternary structures of Escherichia coli DNA-dependent RNA polymerase holenzyme (alpha 2 beta beta' sigma) and core enzyme (alpha 2 beta beta') have been investigated by chemical cross-linking with a cleavable bifunctional reagent, methyl 4-mercaptobutyrimidate, and noncleavable reagents, dimethyl suberimidate and N,N'-(1,4-phenylene)bismaleimide. A model of the subunit organization deduced from cross-linked subunit neighbors identified by dodecyl sulfate-polyacrylamide gel electrophoresis indicates that the large beta and beta' subunits constitute the backbone of both core and holoenzyme, while sigma and two alpha subunits interact with this structure along the contact domain of beta and beta' subunits. In holoenzyme, sigma subunit is in the vicinity of at least one alpha subunit. The two alpha subunits are close to each other in holoenzyme, core enzyme, and the isolated alpha 2 beta complex. Cross-linking of the "premature" core and holoenzyme intermediates in the in vitro reconstitution of active enzyme from isolated subunits suggests that these species are composed of subunit complexes of molecular weight lower than that of native core and holoenzyme, respectively. The structural information obtained for RNA polymerase and its subcomplexes has important implications for the enzyme-promoter recognition as well as the mechanism of subunit assembly of the enzyme.     

Subunit interactions involved in the assembly of pyridine nucleotide transhydrogenase in the membranes of Escherichia coli.

The pyridine nucleotide transhydrogenase (PNT) of Escherichia coli consists of two different subunits (alpha and beta) and assembles as a tetramer (alpha 2 beta 2) in the inner membrane. The pnt genes from E. coli have been cloned on a multicopy plasmid resulting in high level expression of the enzyme activity. We have studied the influence of the different segments of the polypeptide chains of the alpha and beta subunits on the assembly and function of the enzyme by constructing a series of deletion mutants for both of the subunits. Our results show that the assembly of the beta subunit is contingent upon the insertion of the alpha subunit into the membrane, while the alpha subunit can assemble independently of the beta subunit. All deletions constructed for the cytosolic portion of the alpha subunit gave no incorporation of the alpha subunit and, as a consequence, of the beta subunit, also. Of the four membrane-spanning regions of the alpha subunit, the last two were indispensable, while the deletion of the first two still allowed the association of alpha as well as of the beta subunit with the membrane. However, the enzyme was not functional. The two subunits were also loosely associated as mild detergent treatment released them from the membrane in contrast with the wild-type enzyme. Deletions within the beta subunit had little effect on the assembly of the alpha subunit, although less was incorporated. All deletions involving the cytosolic portion of the beta subunit resulted in loss of incorporation into the membrane. Of the eight membrane-spanning regions of the beta subunit, the deletion of regions 2-3, 2-4, 2-6, and 2-7 yielded significant association of both the subunits with the membrane. However, none of these mutants assembled a functional enzyme, and again the two subunits were loosely associated with the membrane. Based on the stringent requirement of the cytosolic portions of alpha and beta subunits for assembly, a model is proposed that suggests interactions between these two regions must occur prior to assembly.     

Pike eel (Muraenesox cinereus) gonadotropin. Amino acid sequences of both alpha and beta subunits

The amino acid sequences of pike eel gonadotropin alpha and beta subunits have been determined by standard sequencing analytical methods. The alpha subunit is composed of 93 amino acid residues while the beta subunit comprises 113 amino acid residues. All the invariant half-cystine residues are in the same positions as those found in other gonadotropins. It is noteworthy that the first, putative glycosylation site (Asn56) found in the alpha subunit of other gonadotropins was replaced by Asp56 in the alpha subunit of pike eel gonadotropin. Similarity analyses indicate that both subunits are structurally more similar to other known fish gonadotropin subunits than to those of the mammalian gonadotropins.     

Dihydropyridine binding of the calcium channel complex from skeletal muscle is modulated by subunit interaction.

The dihydropyridine-binding subunit alpha 1 of the calcium channel complex from rabbit skeletal muscle can be partially depleted from the alpha 2 delta beta-complex using wheat germ agglutinin-affinity chromatography. This depletion of the alpha 1 from the other subunits leads to a loss of dihydropyridine-binding, which can be fully reconstituted by repletion of the alpha 1 with the other subunits. Reassembly of these subunits results in an increase in the Kd and Bmax of the dihydropyridine-binding indicating that the non-dihydropyridine-binding subunits influence dihydropyridine-binding. The affinity of the alpha 1 subunit for the other subunits was determined to be approximately 35 nM. Since the free alpha 1 subunit will not bind to the beta subunit alone, there is evidence, given the selective partitioning of the beta subunit to the lectin-bound subunit pool, that either beta binds with higher affinity to the alpha 2 delta-complex than to the free alpha 1 subunit or that the bound alpha 1 creates or modulates beta-binding. This indicates a functional high affinity interaction between the dihydropyridine-binding alpha 1 subunit and the alpha 2 delta beta-complex.