Structural and dynamic requirements for optimal activity of the essential bacterial enzyme dihydrodipicolinate synthase

Dihydrodipicolinate synthase (DHDPS) is an essential enzyme involved in the lysine biosynthesis pathway. DHDPS from E. coli is a homotetramer consisting of a 'dimer of dimers', with the catalytic residues found at the tight-dimer interface. Crystallographic and biophysical evidence suggest that the dimers associate to stabilise the active site configuration, and mutation of a central dimer-dimer interface residue destabilises the tetramer, thus increasing the flexibility and reducing catalytic efficiency and substrate specificity. This has led to the hypothesis that the tetramer evolved to optimise the dynamics within the tight-dimer. In order to gain insights into DHDPS flexibility and its relationship to quaternary structure and function, we performed comparative Molecular Dynamics simulation studies of native tetrameric and dimeric forms of DHDPS from E. coli and also the native dimeric form from methicillin-resistant Staphylococcus aureus (MRSA). These reveal a striking contrast between the dynamics of tetrameric and dimeric forms. Whereas the E. coli DHDPS tetramer is relatively rigid, both the E. coli and MRSA DHDPS dimers display high flexibility, resulting in monomer reorientation within the dimer and increased flexibility at the tight-dimer interface. The mutant E. coli DHDPS dimer exhibits disorder within its active site with deformation of critical catalytic residues and removal of key hydrogen bonds that render it inactive, whereas the similarly flexible MRSA DHDPS dimer maintains its catalytic geometry and is thus fully functional. Our data support the hypothesis that in both bacterial species optimal activity is achieved by fine tuning protein dynamics in different ways: E. coli DHDPS buttresses together two dimers, whereas MRSA dampens the motion using an extended tight-dimer interface.     

Molecular evolution of an oligomeric biocatalyst functioning in lysine biosynthesis

Dihydrodipicolinate synthase (DHDPS) is critical to the production of lysine through the diaminopimelate (DAP) pathway. Elucidation of the function, regulation and structure of this key class I aldolase has been the focus of considerable study in recent years, given that the dapA gene encoding DHDPS has been found to be essential to bacteria and plants. Allosteric inhibition by lysine is observed for DHDPS from plants and some bacterial species, the latter requiring a histidine or glutamate at position 56 (Escherichia coli numbering) over a basic amino acid. Structurally, two DHDPS monomers form the active site, which binds pyruvate and (S)-aspartate β-semialdehyde, with most dimers further dimerising to form a tetrameric arrangement around a solvent-filled centre cavity. The architecture and behaviour of these dimer-of-dimers is explored in detail, including biophysical studies utilising analytical ultracentrifugation, small-angle X-ray scattering and macromolecular crystallography that show bacterial DHDPS tetramers adopt a head-to-head quaternary structure, compared to the back-to-back arrangement observed for plant DHDPS enzymes. Finally, the potential role of pyruvate in providing substrate-mediated stabilisation of DHDPS is considered.     

Structure and evolution of a novel dimeric enzyme from a clinically important bacterial pathogen

Dihydrodipicolinate synthase (DHDPS) catalyzes the first committed step of the lysine biosynthetic pathway. The tetrameric structure of DHDPS is thought to be essential for enzymatic activity, as isolated dimeric mutants of Escherichia coli DHDPS possess less than 2.5% that of the activity of the wild-type tetramer. It has recently been proposed that the dimeric form lacks activity due to increased dynamics. Tetramerization, by buttressing two dimers together, reduces dynamics in the dimeric unit and explains why all active bacterial DHDPS enzymes to date have been shown to be homo-tetrameric. However, in this study we demonstrate for the first time that DHDPS from methicillin-resistant Staphylococcus aureus (MRSA) exists in a monomer-dimer equilibrium in solution. Fluorescence-detected analytical ultracentrifugation was employed to show that the dimerization dissociation constant of MRSA-DHDPS is 33 nm in the absence of substrates and 29 nm in the presence of (S)-aspartate semialdehyde (ASA), but is 20-fold tighter in the presence of the substrate pyruvate (1.6 nm). The MRSA-DHDPS dimer exhibits a ping-pong kinetic mechanism (k(cat)=70+/-2 s(-1), K(m)(Pyruvate)=0.11+/-0.01 mm, and K(m)(ASA)=0.22+/-0.02 mm) and shows ASA substrate inhibition with a K(si)(ASA) of 2.7+/-0.9 mm. We also demonstrate that unlike the E. coli tetramer, the MRSA-DHDPS dimer is insensitive to lysine inhibition. The near atomic resolution (1.45 A) crystal structure confirms the dimeric quaternary structure and reveals that the dimerization interface of the MRSA enzyme is more extensive in buried surface area and noncovalent contacts than the equivalent interface in tetrameric DHDPS enzymes from other bacterial species. These data provide a detailed mechanistic insight into DHDPS catalysis and the evolution of quaternary structure of this important bacterial enzyme.     

Characterisation of the first enzymes committed to lysine biosynthesis in Arabidopsis thaliana

In plants, the lysine biosynthetic pathway is an attractive target for both the development of herbicides and increasing the nutritional value of crops given that lysine is a limiting amino acid in cereals. Dihydrodipicolinate synthase (DHDPS) and dihydrodipicolinate reductase (DHDPR) catalyse the first two committed steps of lysine biosynthesis. Here, we carry out for the first time a comprehensive characterisation of the structure and activity of both DHDPS and DHDPR from Arabidopsis thaliana. The A. thaliana DHDPS enzyme (At-DHDPS2) has similar activity to the bacterial form of the enzyme, but is more strongly allosterically inhibited by (S)-lysine. Structural studies of At-DHDPS2 show (S)-lysine bound at a cleft between two monomers, highlighting the allosteric site; however, unlike previous studies, binding is not accompanied by conformational changes, suggesting that binding may cause changes in protein dynamics rather than large conformation changes. DHDPR from A. thaliana (At-DHDPR2) has similar specificity for both NADH and NADPH during catalysis, and has tighter binding of substrate than has previously been reported. While all known bacterial DHDPR enzymes have a tetrameric structure, analytical ultracentrifugation, and scattering data unequivocally show that At-DHDPR2 exists as a dimer in solution. The exact arrangement of the dimeric protein is as yet unknown, but ab initio modelling of x-ray scattering data is consistent with an elongated structure in solution, which does not correspond to any of the possible dimeric pairings observed in the X-ray crystal structure of DHDPR from other organisms. This increased knowledge of the structure and function of plant lysine biosynthetic enzymes will aid future work aimed at improving primary production.     

Structural, kinetic and computational investigation of Vitis vinifera DHDPS reveals new insight into the mechanism of lysine-mediated allosteric inhibition

Lysine is one of the most limiting amino acids in plants and its biosynthesis is carefully regulated through inhibition of the first committed step in the pathway catalyzed by dihydrodipicolinate synthase (DHDPS). This is mediated via a feedback mechanism involving the binding of lysine to the allosteric cleft of DHDPS. However, the precise allosteric mechanism is yet to be defined. We present a thorough enzyme kinetic and thermodynamic analysis of lysine inhibition of DHDPS from the common grapevine, Vitis vinifera (Vv). Our studies demonstrate that lysine binding is both tight (relative to bacterial DHDPS orthologs) and cooperative. The crystal structure of the enzyme bound to lysine (2.4 Å) identifies the allosteric binding site and clearly shows a conformational change of several residues within the allosteric and active sites. Molecular dynamics simulations comparing the lysine-bound (PDB ID 4HNN) and lysine free (PDB ID 3TUU) structures show that Tyr132, a key catalytic site residue, undergoes significant rotational motion upon lysine binding. This suggests proton relay through the catalytic triad is attenuated in the presence of lysine. Our study reveals for the first time the structural mechanism for allosteric inhibition of DHDPS from the common grapevine.     

Functional rescue of a bacterial dapA auxotroph with a plant cDNA library selects for mutant clones encoding a feedback-insensitive dihydrodipicolinate synthase

Dihydrodipicolinate synthase (DHDPS; EC4.2.1.52) catalyses the first reaction of lysine biosynthesis in plants and bacteria. Plant DHDPS enzymes are strongly inhibited by lysine (I0.5 approximately 10 microM), whereas the bacterial enzymes are less (50-fold) or insensitive to lysine inhibition. We found that plant dhdps sequences expressing lysine-sensitive DHDPS enzymes are unable to complement a bacterial auxotroph, although a functional plant DHDPS enzyme is formed. As a consequence of this, plant dhdps cDNA clones which have been isolated through functional complementation using the DHDPS-deficient Escherichia coli strain encode mutated DHDPS enzymes impaired in lysine inhibition. The experiments outlined in this article emphasize that heterologous complementation can select for mutant clones when altered protein properties are requisite for functional rescue. In addition, the mutants rescued by heterologous complementation revealed a new critical amino acid substitution which renders lysine insensitivity to the plant DHDPS enzyme. An interpretation is given for the impaired inhibition mechanism of the mutant DHDPS enzyme by integrating the identified amino acid substitution in the DHDPS protein structure.     

Biochemical studies and crystal structure determination of dihydrodipicolinate synthase from Pseudomonas aeruginosa

The intracellular enzyme dihydrodipicolinate synthase (DHDPS, E.C. 4.2.1.52) from Pseudomonas aeruginosa is a potential drug target because it is essential for the growth of bacteria while it is absent in humans. Therefore, in order to design new compounds using structure based approach for inhibiting the function of DHDPS from P. aeruginosa (Ps), we have cloned, characterized biochemically and biophysically and have determined its three-dimensional structure. The gene encoding DHDPS (dapA) was cloned in a vector pET-28c(+) and the recombinant protein was overexpressed in the Escherichia coli host. The K(m) values of the recombinant enzyme estimated for the substrates, pyruvate and (S)-aspartate-β-semialdehyde [(S)-ASA] were found to be 0.90±0.13 mM and 0.17±0.02 mM, respectively. The circular dichroism studies showed that the enzyme adopts a characteristic β/α conformation which is retained up to 65°C. The fluorescence data indicated the presence of exposed tryptophan residues in the enzyme. The three-dimensional structure determination showed that DHDPS forms a homodimer which is stabilized by several hydrogen bonds and van der Waals forces at the interface. The active site formed with residues Thr44, Tyr107 and Tyr133 is found to be stereochemically suitable for catalytic function. It may be noted that Tyr107 of the catalytic triad belongs to the partner molecule in the dimer. The structure of the complex of PsDHDPS with (S)-lysine determined at 2.65 ? resolution revealed the positions of three lysine molecules bound to the protein.     

Exploring the dihydrodipicolinate synthase tetramer: How resilient is the dimer-dimer interface?

Dihydrodipicolinate synthase (DHDPS, E.C. 4.2.1.52) is a tetrameric enzyme that catalyses the first committed step of the lysine biosynthetic pathway. Dimeric variants of DHDPS have impaired catalytic activity due to aberrant protein motions within the dimer unit. Thus, it is thought that the tetrameric structure functions to restrict these motions and optimise enzyme dynamics for catalysis. Despite the importance of dimer-dimer association, the interface between subunits of each dimer is small, accounting for only 4.3% of the total monomer surface area, and the structure of the interface is not conserved across species. We have probed the tolerance of dimer-dimer association to mutation by introducing amino acid substitutions within the interface. All point mutations resulted in destabilisation of the ‘dimer of dimers’ tetrameric structure. Both the position of the mutation in the interface and the physico-chemical nature of the substitution appeared to effect tetramerisation. Despite only weak destabilisation of the tetramer by some mutations, catalytic activity was reduced to ∼10-15% of the wild-type in all cases, suggesting that the dimer-dimer interface is finely tuned to optimise function.     

Effect of single point mutations in a form of systemic amyloidosis

Amyloid deposits of light-chain proteins are associated with the most common form of systemic amyloidosis. We have studied the effects of single point mutations on amyloid formation of these proteins using explicit solvent model molecular dynamics simulations. For this purpose, we compare the stability of the wild-type immunoglobulin light-chain protein REI in its native and amyloid forms with that of four mutants: R61N, G68D, D82I, and A84T. We argue that the experimentally observed differences in the propensity for amyloid formation result from two effects. First, the mutant dimers have a lower stability than the wild-type dimer due to increase exposure of certain hydrophobic residues. The second effect is a shift in equilibrium between monomers with amyloid-like structure and such with native structures. Hence, when developing drugs against light-chain associated systemic amyloidosis, one should look for components that either stabilize the dimer by binding to the dimer interface or reduce for the monomers the probability of the amyloid form.     

Insights into subunit interactions in the heterotetrameric structure of potato ADP-glucose pyrophosphorylase

ADP-glucose pyrophosphorylase, a key allosteric enzyme involved in higher plant starch biosynthesis, is composed of pairs of large (LS) and small subunits (SS). Current evidence indicates that the two subunit types play distinct roles in enzyme function. The LS is involved in mainly allosteric regulation through its interaction with the catalytic SS. Recently the crystal structure of the SS homotetramer has been solved, but no crystal structure of the native heterotetrameric enzyme is currently available. In this study, we first modeled the three-dimensional structure of the LS to construct the heterotetrameric enzyme. Because the enzyme has a 2-fold symmetry, six different dimeric (either up-down or side-by-side) interactions were possible. Molecular dynamics simulations were carried out for each of these possible dimers. Trajectories obtained from molecular dynamics simulations of each dimer were then analyzed by the molecular mechanics/Poisson-Boltzmann surface area method to identify the most favorable dimers, one for up-down and the other for side-by-side. Computational results combined with site directed mutagenesis and yeast two hybrid experiments suggested that the most favorable heterotetramer is formed by LS-SS (side-by-side), and LS-SS (up-down). We further determined the order of assembly during the heterotetrameric structure formation. First, side-by-side LS-SS dimers form followed by the up-down tetramerization based on the relative binding free energies.     

The crystal structure of ZapA and its modulation of FtsZ polymerisation

FtsZ is part of a mid-cell cytokinetic structure termed the Z-ring that recruits a hierarchy of fission related proteins early in the bacterial cell cycle. The widely conserved ZapA has been shown to interact with FtsZ, to drive its polymerisation and to promote FtsZ filament bundling thereby contributing to the spatio-temporal tuning of the Z-ring. Here, we show the crystal structure of ZapA (11.6 kDa) from Pseudomonas aeruginosa at 2.8 A resolution. The electron density reveals two dimers associating via an extensive C-terminal coiled-coil protrusion to form an elongated anti-parallel tetramer. In solution, ZapA exists in a dimer-tetramer equilibrium that is strongly correlated with concentration. An increase in concentration promotes formation of the higher oligomeric state. The dimer is postulated to be the predominant physiological species although the tetramer could become significant if, as FtsZ is integrated into the Z-ring and is cross-linked, the local concentration of the dimer becomes sufficiently high. We also show that ZapA binds FtsZ with an approximate 1:1 molar stoichiometry and that this interaction provokes dramatic FtsZ polymerisation and inter-filament association as well as yielding filaments, single or bundled, more stable and resistant to collapse. Whilst in vitro dynamics of FtsZ are well characterised, its in vivo arrangement within the ultra-structural architecture of the Z-ring is yet to be determined despite being fundamental to cell division. The ZapA dimer has single 2-fold symmetry whilst the bipolar tetramer displays triple 2-fold symmetry. Given the symmetry of these ZapA oligomers and the polar nature of FtsZ filaments, the structure of ZapA carries novel implications for the inherent architecture of the Z-ring in vivo.     

Structural and functional characterization of Staphylococcus aureus dihydrodipicolinate synthase

Lysine biosynthesis is crucial for cell-wall formation in bacteria. Enzymes involved in lysine biosynthesis are thus potential targets for anti-microbial therapeutics. Dihydrodipicolinate synthase (DHDPS) catalyzes the first step of this pathway. Unlike its homologues, Staphylococcus aureus DHDPS is a dimer both in solution and in the crystal and is not feedback inhibited by lysine. The crystal structure of S. aureus DHDPS in the free and substrate bound forms provides a structural rationale for its catalytic mechanism. The structure also reveals unique conformational features of the S. aureus enzyme that could be crucial for the design of specific non-competitive inhibitors.     

Black fungi and associated bacterial communities in the phyllosphere of grapevine

In this study we investigate bacterial communities in association with an enriched black-fungal community in the plant phyllosphere to test whether these fungi create an environment for specific bacteria. Under organic conditions of agriculture, grapevine plants (Vitis vinifera) display an increased occurrence of the black fungi Aureobasidium pullulans and Epicoccum nigrum. Their enrichment agrees with the tolerance of these fungi to copper and sulphate, both used as main fungicides in organic viticulture. Both fungi also intrude the plant material to grow endophytically. Bacterial communities associated with black fungi of the plant surface and endosphere showed no differences compared to those found in conventionally managed V. vinifera plants. This suggests that despite an increase of these black fungi in organic practice, they do not shape bacterial diversity in grapevine plants. Nevertheless, dual cultures revealed a negative effect of Aureobasidium on the growth of certain bacilli, whereas growth of Aureobasidium was impeded by one Pseudomonas strain. Such singular effects are either not apparent in the natural black-fungal--bacterial community of the grape phyllosphere or are of rather localized effect.     

Structure of a murine cytoplasmic serine hydroxymethyltransferase quinonoid ternary complex: evidence for asymmetric obligate dimers

Serine hydroxymethyltransferase (SHMT) is a pyridoxal phosphate-dependent enzyme that catalyzes the reversible conversion of serine and tetrahydrofolate to glycine and methylenetetrahydrofolate. This reaction generates single carbon units for purine, thymidine, and methionine biosynthesis. The enzyme is a homotetramer comprising two obligate dimers and four pyridoxal phosphate-bound active sites. The mammalian enzyme is present in cells in both catalytically active and inactive forms. The inactive form is a ternary complex that results from the binding of glycine and 5-formyltetrahydrofolate polyglutamate, a slow tight-binding inhibitor. The crystal structure of a close analogue of the inactive form of murine cytoplasmic SHMT (cSHMT), lacking only the polyglutamate tail of the inhibitor, has been determined to 2.9 A resolution. This first structure of a ligand-bound mammalian SHMT allows identification of amino acid residues involved in substrate binding and catalysis. It also reveals that the two obligate dimers making up a tetramer are not equivalent; one can be described as "tight-binding" and the other as "loose-binding" for folate. Both active sites of the tight-binding dimer are occupied by 5-formyltetrahydrofolate (5-formylTHF), whose N5-formyl carbon is within 4 A of the glycine alpha-carbon of the glycine-pyridoxal phosphate complex; the complex appears to be primarily in its quinonoid form. In the loose-binding dimer, 5-formylTHF is present in only one of the active sites, and its N5-formyl carbon is 5 A from the glycine alpha-carbon. The pyridoxal phosphates appear to be primarily present as geminal diamine complexes, with bonds to both glycine and the active site lysine. This structure suggests that only two of the four catalytic sites on SHMT are catalytically competent and that the cSHMT-glycine-5-formylTHF ternary complex is an intermediate state analogue of the catalytic complex associated with serine and glycine interconversion.     

Dihydrodipicolinate synthase from Thermotoga maritima

DHDPS (dihydrodipicolinate synthase) catalyses the branch point in lysine biosynthesis in bacteria and plants and is feedback inhibited by lysine. DHDPS from the thermophilic bacterium Thermotoga maritima shows a high level of heat and chemical stability. When incubated at 90 degrees C or in 8 M urea, the enzyme showed little or no loss of activity, unlike the Escherichia coli enzyme. The active site is very similar to that of the E. coli enzyme, and at mesophilic temperatures the two enzymes have similar kinetic constants. Like other forms of the enzyme, T. maritima DHDPS is a tetramer in solution, with a sedimentation coefficient of 7.2 S and molar mass of 133 kDa. However, the residues involved in the interface between different subunits in the tetramer differ from those of E. coli and include two cysteine residues poised to form a disulfide bond. Thus the increased heat and chemical stability of the T. maritima DHDPS enzyme is, at least in part, explained by an increased number of inter-subunit contacts. Unlike the plant or E. coli enzyme, the thermophilic DHDPS enzyme is not inhibited by (S)-lysine, suggesting that feedback control of the lysine biosynthetic pathway evolved later in the bacterial lineage.     

Protein conformational heterogeneity as a binding catalyst: ESI-MS study of hemoglobin H formation

Our previous studies of hemoglobin tetramer assembly in vitro suggested that the initial step in the oligomerization process, which ultimately dictates the high fidelity of the heterotetramer (alpha*beta*)2 assembly, is the binding of a flexible heme-free beta-globin chain to a highly ordered heme-bound alpha*-globin. In this work, we extend these studies to investigate formation of the homotetrameric hemoglobin H, whose formation in vivo is a well-documented clinical consequence of significant overexpression of beta-globin in alpha-thalassemic disorders. Upon reconstitution of the isolated beta-globin with excess heme, the predominant species in the ESI mass spectrum corresponds to the homotetramer beta*4, alongside homodimeric species and monomeric beta-globin chains in both apo and holo forms. The assembly process of the hemoglobin H homotetramer apparently follows a scenario similar to that of a normal heterodimeric hemoglobin (alpha*beta*)2 species, with the asymmetric binding event between compact and flexible polypeptide chains being the initial step. The extreme importance of large-scale chain dynamics and conformational heterogeneity for the protein assembly process is highlighted by the inability of highly structured alpha-globins to undergo ordered oligomerization to form dimers and tetramers as opposed to indiscriminate aggregation.     

Loop-driven conformational transition between the alternative and collapsed form of prethrombin-2: targeted molecular dynamics study

Two distinct crystal structures of prethrombin-2, the alternative and collapsed forms, are elucidated by X-ray crystallogrphy. We analyzed the conformational transition from the alternative to the collapsed form employing targeted molecular dynamics (TMD) simulation. Despite small RMSD difference in the two X-ray crystal structures, some hydrophobic residues (W60d, W148, W215, and F227) show a significant difference between the two conformations. TMD simulation shows that the four hydrophobic residues undergo concerted movement from dimer to trimer transition via tetramer state in the conformational change from the alternative to the collapsed form. We reveal that the concerted movement of the four hydrophobic residues is controlled by movement of specific loop regions behind. In this paper, we propose a sequential scenario for the conformational transition from the alternative form to the collapsed form, which is partially supported by the mutant W148A simulation.     

The conformational feasibility for the formation of reaching dimer in ASV and HIV integrase: a molecular dynamics study

Retroviral integrases are reported to form alternate dimer assemblies like the core–core dimer and reaching dimer. The core–core dimer is stabilized predominantly by an extensive interface between two catalytic core domains. The reaching dimer is stabilized by N-terminal domains that reach to form intermolecular interfaces with the other subunit’s core and C-terminal domains (CTD), as well as CTD–CTD interactions. In this study, molecular dynamics (MD), Brownian dynamics (BD) simulations, and free energy analyses, were performed to elucidate determinants for the stability of the reaching dimer forms of full-length Avian Sarcoma Virus (ASV) and Human Immunodeficiency Virus (HIV) IN, and to examine the role of the C-tails (the last ~16–18 residues at the C-termini) in their structural dynamics. The dynamics of an HIV reaching dimer derived from small angle X-ray scattering and protein crosslinking data, was compared with the dynamics of a core–core dimer model derived from combining the crystal structures of two-domain fragments. The results showed that the core domains in the ASV reaching dimer express free dynamics, whereas those in the HIV reaching dimer are highly stable. BD simulations suggest a higher rate of association for the HIV core–core dimer than the reaching dimer. The predicted stability of these dimers was therefore ranked in the following order: ASV reaching dimer < HIV reaching dimer < composite core–core dimer. Analyses of MD trajectories have suggested residues that are critical for intermolecular contacts in each reaching dimer. Tests of these predictions and insights gained from these analyses could reveal a potential pathway for the association and dissociation of full-length IN multimers.     

Evolution of quaternary structure in a homotetrameric enzyme

Dihydrodipicolinate synthase (DHDPS) is an essential enzyme in (S)-lysine biosynthesis and an important antibiotic target. All X-ray crystal structures solved to date reveal a homotetrameric enzyme. In order to explore the role of this quaternary structure, dimeric variants of Escherichia coli DHDPS were engineered and their properties were compared to those of the wild-type tetrameric form. X-ray crystallography reveals that the active site is not disturbed when the quaternary structure is disrupted. However, the activity of the dimeric enzymes in solution is substantially reduced, and a tetrahedral adduct of a substrate analogue is observed to be trapped at the active site in the crystal form. Remarkably, heating the dimeric enzymes increases activity. We propose that the homotetrameric structure of DHDPS reduces dynamic fluctuations present in the dimeric forms and increases specificity for the first substrate, pyruvate. By restricting motion in a key catalytic motif, a competing, non-productive reaction with a substrate analogue is avoided. Small-angle X-ray scattering and mutagenesis data, together with a B-factor analysis of the crystal structures, support this hypothesis and lead to the suggestion that in at least some cases, the evolution of quaternary enzyme structures might serve to optimise the dynamic properties of the protein subunits.