Architecture and regulation of filamentous human cystathionine beta-synthase

Cystathionine beta-synthase (CBS) is an essential metabolic enzyme across all domains of life involved in the production of glutathione, cysteine, and hydrogen sulphide1–4. Human CBS appends to its conserved catalytic domain a regulatory domain that modulates activity by S-adenosyl-L-methionine (SAM) and promotes oligomerization5–12, however the molecular basis is unknown. Here we show using cryo-electron microscopy that full-length human CBS in the basal and SAM-bound activated states polymerises as filaments mediated by a conserved regulatory domain loop. In the basal state, CBS regulatory domains sterically block the catalytic domain active site, resulting in a low activity filament with three CBS dimers per turn. This steric block is removed when in the activated state, one molecule of SAM binds to the regulatory domain, forming a high activity filament with two CBS dimers per turn. These large conformational changes result in a central filament of SAM stabilised regulatory domains at the core, decorated with highly flexible catalytic domains. Polymerization stabilises CBS and increases the cooperativity of allosteric activation by SAM. Together our findings elaborate our understanding of CBS enzyme regulation, and open new avenues for investigating the pathogenic mechanism and therapeutic opportunities for CBS-associated disorders3,13–17.


cryo-electron microscopy that full-length human CBS in the basal and SAM-bound activated states polymerises as filaments mediated by a conserved regulatory domain loop.
In the basal state, CBS regulatory domains sterically block the catalytic domain active site, resulting in a low activity filament with three CBS dimers per turn. This steric block is removed when in the activated state, one molecule of SAM binds to the regulatory domain, forming a high activity filament with two CBS dimers per turn. These large conformational changes result in a central filament of SAM stabilised regulatory domains at the core, decorated with highly flexible catalytic domains. Polymerization stabilises CBS and increases the cooperativity of allosteric activation by SAM. Together our findings elaborate our understanding of CBS enzyme regulation, and open new avenues for investigating the pathogenic mechanism and therapeutic opportunities for CBS-associated disorders 3,13-17 .
The pyridoxal 5'-phosphate (PLP)-dependent enzyme CBS 18 catalyses the condensation of serine and homocysteine to form cystathionine. Playing a pivotal role in the transsulfuration pathway and redox regulation 18 and being linked to one carbon metabolism, CBS produces cysteine, glutathione as well as the gaseous transmitter hydrogen sulphide 1 (H2S). CBS has recently gained interest as a therapeutic target as inhibition of H2S production has been suggested for treatment of specific cancers 16 and Down's Syndrome 15 . Inherited lost-offunction mutations of CBS result in classical homocystinuria (HCU), the most common inborn error of sulphur metabolism 17 . Classical homocystinuria has been recognised as a protein misfolding disorder as many of the known pathogenic mutations result in aggregation and degradation of the CBS enzyme 19,20 .
Human CBS adopts a unique multi-domain structure: an N-terminal heme binding domain (residues 38-74), a central PLP-dependent catalytic domain (CD, residues 75-382), and a C-terminal regulatory domain (RD, residues 411-551) 2,5,10 (Fig. 1a). The RD adopts the evolutionarily conserved Bateman module, consisting of two tandem CBS motifs (CBS-1 and CBS-2) and a surface-exposed loop (residues 516-525) extending from a CBS-2 motif (Extended Data Fig. 1a). Bateman modules act as a regulatory sensor in response to the binding of predominantly adenosine-containing ligands 21 , and are present in enzymes across the three domains of life 22 . In mammals, the activity of CBS is increased by the binding of SAM to the Bateman module 23 . The enzyme is therefore proposed to transition between the basal state in the absence of SAM, and the SAM-bound activated state 23 Crystal structures of human CBS 10,8,9 have been determined of CD alone (CBS CD ), of full-length protein engineered with the RD loop deletion (CBS Δ516-525 ) 8,12 , and of RD alone with the loop deletion (CBS RDΔ516-525 ) complexed with SAM. Together, they depicted human CBS as a homodimer, where both CD and RD can dimerise independently. The structural data also revealed the molecular mechanism of SAM activation, whereby the Bateman module in the RD acts as an autoinhibitory cap to the CD, and upon binding SAM undergoes a conformational change relieving the inhibition to allow active site access for catalysis (Extended Data Fig. 1) 9,10 . However, these structures do not take into account various reports that the RD promotes the formation of CBS tetramers and higher order oligomers with a high tendency to aggregate 7,24-26 . Indeed, CBS oligomerization and SAM response varies across the animal kingdom 6 ; it is unclear how human CBS oligomerises and its relation to SAM allosteric regulation is unknown 21,22 .
Additionally, mutations on or deletion of the Bateman module can rescue the most common homocystinuria associated mutations, but the structural information so far has given limited insight [27][28][29] . Efforts have also been made on developing new small molecule therapies targeting CBS 3,14,15 , but the lack of full-length enzyme structure has been a possible hinderance. Here we used a combination of biophysical techniques and cryo-electron microscopy showing that human CBS full-length protein polymerises as a filament adopting two very different morphologies dependent on SAM binding, and that polymerization plays a role in both enzyme activation and stability.
Cryo-EM of full-length human CBS reveals a filamentous architecture. We pursued the cryo-electron microscopy structure of full-length CBS initially using two constructs: one where an N-terminal His-tag was removed during purification (CBS FL ), and one with a permanent Cterminal His-tag (CBS FL-CHis ) (Extended Data Fig. 2a). In analytical gel filtration on a Superose 6 column, both CBS FL and CBS FL-CHis proteins eluted as a broad peak, suggestive of different oligomeric states with molecular weights larger than tetramers (Extended Data Fig. 2b). Similar observations of larger-than-tetrameric CBS FL oligomers, and even higher molecular weight oligomers for CBS FL-CHis , were made in Coomassie-stained clear-native and blue-native PAGE experiments (Extended Fig. 2c, d). As control, CBS Δ516-525 , CBS CD , and CBS RDΔ516-525 behaved as expected dimers 30 . Micrographs of full-length CBS from both constructs in vitreous ice clearly showed the presence of flexible filaments ( Supplementary Fig. 1a, 3a) of varying lengths agreeing with 2D classes (Fig. 1b, Supplementary Fig. 1b, 3b). Multiple maps were processed using both helical ( Supplementary Fig. 1, 3) and single particle (Supplementary Fig. 2,4) reconstruction to resolutions of between 3.9 to 3.0 Å. Both constructs resulted in maps with virtually identical conformations (Extended Data Fig. 3a), and both were used for modelling.
The CBS filament adopts a left-handed helical architecture with a twist of -108° and rise of 51 Å (Fig. 1c, Supplementary Fig. 1, 3). The domain-swapped dimer, previously observed in crystal structures, is the repeating unit and helical formation is driven by inter-ic RD interactions, i.e., between the RDs of neighbouring s of the filament. Here the RD sits atop the active site entrance of the catalytic domain hindering substrate access (Fig. 1c, e). Loop 516-525, a β-turn-β extension from the CBS-2 motif in the conserved Bateman module, plays a key role in driving oligomerization. Specifically, one RD each from two neighbouring CBS s interact in a butterfly-like dimeric arrangement, related by C2 symmetry, such that the loop 516-525 from a RD of one dimer forms a clasp around a RD of the neighbouring dimer. This packing arrangement, burying a total surface area of ~1550 Å 2 (Fig. 1e, f, Extended Data Fig.  3b), is stabilised through two interfaces composed entirely of the RDs. The first interface is between the CBS-2 and CBS-1 motifs, involving loop 516-525 of one dimeric subunit and αhelix 15 of the neighbouring dimeric subunit. Here, main-chain interactions are mediated between β-strand 12 residues 516-519 of one RD and β-strand 8 residues 422-426 of the adjacent RD (Fig. 1f, Extended Data Fig. 3d). This arrangement results in residue Tyr518 from the oligomerization loop slotting into a hydrophobic pocket formed by Leu423, Val425, Ile429, and Ile437 of α-helix 15 (Extended Data Fig. 3d). The second interface involves inter-ic RD contacts, between the two neighbouring CBS-2 motifs. Here RD residues Leu419, Leu492, Met529, and Phe531 of one dimeric subunit form hydrophobic packing interactions with the equivalent residues of the neighbouring dimeric subunit (Extended Data Fig. 3e). Due to these interactions both Ala421 and Pro422 are shifted from their positions as observed in the previous crystal structures of CBS Δ516-525 (Extended Data Fig. 3f) [8][9][10] . Altogether, the two modes of inter-dimeric RD interactions demonstrate how the loop 516-525 is the main driver of CBS oligomerization 10,13,20,29 . b, Initial representative 2D classes of CBS in the basal state. c, Cryo-EM helical reconstruction of the CBS filament in the basal state at a resolution of 3.9 Å. Individual domain swapped dimers are numbered. d, Single particle reconstruction focused on one CBS dimer unit at a resolution of 3.0 Å. One monomer is coloured as in Fig. 1a.

CBS degrades into tetramers and dimers.
Though both full-length CBS constructs resulted in highly similar filament maps, one key difference was the observed protein degradation and the presence of slightly shorter oligomers of the CBS FL construct without a permanent His-tag (Extended Data Fig. 2a, b). Consequently, along with the filament classes we observed 2D averages of this construct that represented these degradation products (Extended Data Fig.  4a, b). One collection of classes appeared to be the catalytic domain dimer alone, suggesting that the RD was degraded from some full-length protein, although we could not obtain a reasonable reconstruction due to its small size (~80 kDa) (Extended Data Fig. 4a). Another collection of classes resulted in a 3.8 Å map of a degraded CBS tetramer (Extended Data Fig.  4a, b, Supplementary Fig.4). Here two degraded heterodimers, composed of one full-length protomer and one RD-degraded catalytic domain protomer (Extended Data Fig. 4b), interact through a single Bateman-Bateman interface, highly similar to the arrangement seen in the intact filament. The degradation of the RD renders the active site loops within the catalytic domain of the full-length CBS in a more opened state (Extended Data Fig. 4c).
SAM binding transforms the morphology of the CBS filament. The global methyl donor SAM functions as an allosteric activator of human CBS activity 23 . In our biophysical characterisation assays (Extended Fig. 2c, d), SAM had no significant effect on the oligomeric status of all CBS constructs, agreeing with previous reports 12,31 . Since oligomerization occurs without SAM, we hypothesised that SAM could modulate the morphology of the CBS filament, as part of its role as an allosteric activator. To this end, cryo-EM was used to analyse CBS FL-CHis in the presence of SAM. Micrographs showed that CBS retains a filamentous architecture in the presence of SAM, but with a significantly altered morphology as shown by 2D classes (Fig. 2a, Supplementary Fig. 5a, c). Obtaining a 3D reconstruction took considerable effort due to the highly flexible nature of the filaments ( Supplementary Fig. 5b). Through helical refinement we generated a global map at 4.0 Å resolution which reveals a central helical stalk decorated with highly flexible lobes (Fig 2b). To aid in model building, we applied masks and performed local refinement that resulted in local maps for the central stalk at 4.1 Å resolution and for the flexible domain at 8.3 Å resolution ( Supplementary Fig. 6).
These maps allowed us to model the entire filament, by docking one catalytic domain dimer into each flexible lobe (PDB: 4PCU), and repeating units of the regulatory domain dimer (PDB: 4UUU) into the central stalk. The overall morphology of the resulting filament is drastically different in comparison to the basal state, as reflected by the 66% increase in twist (-178.6°) and 10% decrease in rise (46.9 Å) of the filament in the presence of SAM (Fig. 2b, Extended Data Fig. 5a). Previous crystal structures of the non-filamentous CBS Δ516-525 dimers 9,10 showed that SAM binding to the RD elicits its dis-association from the CD and subsequently its homo-dimerization, thereby freeing the active site access for catalysis (Extended Data Fig. 1a). In the context of the full-length enzyme elucidated here, the SAMmediated conformational change creates a central filament stalk composed of repeating units of the SAM-bound RD dimer, arranged in an antiparallel "daisy-chain" like fashion due to the interactions of the loop 516-525 with the neighbouring subunit (Fig. 2b, c). The central filament stalk is decorated by highly flexible CDs, where the active site entrance loops are free to open and hence increase the accessibility for substrates (Extended Data Fig. 5b) 9 .
Comparing our basal and activated filaments, the SAM-mediated conformational change to the RD is highly agreeable with that observed in the crystal structures of CBS Δ516-525 dimers where there is a relative 18° rotation between the CBS-1 and CBS-2 motifs caused by SAM binding (Fig. 2d) 9,10 . Observing this interface of CBS-1 and CBS-2 in isolation, the conformational change is mainly localised in the CBS-1 motif and appears as an unfurling of the "butterfly wings" of this dimeric arrangement (Movie 1). This results in α-helix 15 displaced by 8 Å and α-helix 16 by as much as 11 Å from their original positions. Interestingly loop 516-525 from the neighbouring subunit also moves 3.0 Å to maintain its interactions with residues 422-426 and α-helix 15 (Fig. 2d). Additionally, alignment to the central helical Z-axis and a simple morph of the global basal and activated models show that the large conformational change is possible in the filament with little clashes when the CD moves in concert with the RDs (Extended Data Fig. 5d, Movie 2) 9,10 . Bateman interface in the basal and activated states showing the conformational change due to SAM binding.

Filament formation does not create more SAM binding sites in CBS.
Each Bateman module, assembled from the tandem CBS-1 and CBS-2 motifs, contains in principle two ligand-binding sites (S1 and S2) related by dyad symmetry 8 . In our activated filament maps, ligand density was present for SAM only at the S2 site (Fig. 2b, 3a). No apparent density was found for SAM at the S1 site nor at the filament interfaces. This 1:1 (one SAM to one CBS protomer) stoichiometry is identical to previously observed CBS Δ516-525 crystal structures where only the S2 site was occupied by SAM 9,10 . These structures suggest that Phe443 and Asp538 at the S2 site are key residues in SAM binding 10 . Therefore, to confirm the 1:1 binding of SAM we purified the mutants F443A and D538A, and initially tested their enzymatic response to SAM. These mutants showed a low basal activity like wild-type, but unlike wildtype could not be stimulated by SAM (Fig. 3b). We next performed isothermal titration calorimetry (ITC) of wild-type CBS FL-CHis against SAM which demonstrated two apparent binding events at ~160 nM and ~600 nM, in agreement with previous reports 11,12,31 . In contrast the S2 site mutations, F443A and D538A, eliminated both SAM binding events (Fig. 3c, Extended Data Fig. 6b, d), again suggesting that no other SAM sites exist in the filament. We reasoned that the two apparent binding events are attributed to the binding of one SAM to the S2 site and the resulting conformational rearrangement into the activated state. In support of this interpretation, ITC of CBS FL and CBS Δ516-525 (where the protein can respond to both ligand binding and conformational changes) both demonstrated two apparent binding events, whereas the RD alone protein CBS RDΔ516-525 (which only responds to ligand binding) presented only one event at ~4 μM (Extended Data Fig. 6c, d). Overall, our data indicates that CBS binds SAM in a 1:1 manner, and that filament formation does not create additional SAM binding sites.

Filament formation increases cooperativity of SAM activation and CBS stability.
Polymerization of metabolic enzymes, such as involving filament formation, has been linked to their regulation and stabilization 32,33 , and we hypothesised that the assembly of human CBS into a filament could play a similar role that facilitates enzyme catalysis. Our observation of loop 516-525 moving in tandem with the conformational change of α-helix 15 (Fig. 2d), in the presence of SAM, suggests potential crosstalk communication between regulatory domains from neighbouring CBS proteins (inter-dimer) in the filament (Movie 1). To investigate potential cooperativity within the CBS filament, we characterised CBS activity by measuring H2S production from the condensation of cysteine and homocysteine. Km values for both homocysteine and cysteine were essentially identical for the four constructs at ~0.3 and ~20 mM respectively. CBS FL , CBS FL-CHis , and CBS Δ516-525 were allosterically activated by SAM whereas CBS CD was not (Extended Data Fig 6a). By titrating SAM, we found that the responsive constructs showed a ~2-fold increase in activity, exhibiting Kact for SAM of ~26.0-36.0 µM (Fig. 3a, Extended Data Fig 6b) agreeing with reported values 11,25,34 . The activation of CBS FL and CBS FL-CHis was cooperative with a Hill coefficient (nHill) of 3.0-3.6, whereas the non-filamentous CBS Δ516-525 presented a lower nHill of 2.0 ( Fig. 3a, Extended Data Fig 6b). Next, we determined if filament formation alters CBS stability by using thermal shift. The CBS Δ516-525 protein, which does not form filaments, is less thermostable than CBS FL by ~5 °C, confirming that filamentation increases stability. We also found that CBS FL-CHis is more thermostable than CBS FL by ~3 °C (Fig. 3b, Extended Data Fig. 5a), which may be due in part to it forming longer oligomers and being less degraded than CBS FL (Extended Data Fig. 2) 30 . Moreover, it is known that the activity of human CBS can be increased by thermal activation, likely due to the denaturation of the regulatory domain that relieves its autoinhibitory effect 7,11,23 . Repeating this assay, on both CBS FL and CBS Δ516-525 we determined Tm values of 49.5 °C and 43.7 °C respectively showing that CBS Δ516-525 is more prone to thermal activation and that its regulatory domain is less stable (Fig. 3c). These findings suggest that polymerization alters both the cooperativity of SAM activation and stabilizes the regulatory domain probably to maintain CBS in the basal state conformation.

Discussion
Conflicting reports of human CBS oligomerization, evidenced by a variety of biophysical and immunoblotting techniques, using both recombinant and endogenous sources of the protein, have plagued the literature since its initial characterisation 5,12,20,[24][25][26]35,36 . Here we have shown that human CBS oligomerises into filaments, adopting (at least) two distinct architectures respectively for the basal and activated states. Chiefly our findings reflect the initial reports of CBS purified from human liver, where it was shown to form large oligomers with a tendency to both aggregate and degrade to a more active state 26 . This discovery of filamentation evaded past crystallographic studies involving an engineered protein that removes a surface loop (residues 516-525) 8-10 now revealed to be key to polymerization, alongside the assumption that CBS is predominantly a tetrameric protein 6 . Our observation of CBS filaments with heterogenous lengths in cryo-EM micrographs therefore sufficiently explains previous findings of a mixture of CBS oligomers. Due to this heterogeneity the reported tetrameric state of CBS is likely to be two dimers interacting through a single Bateman module pair but additionally could also be formed via the degradation of the Bateman module that we have shown here (Extended Data Fig. 4).
The link between the oligomeric state and SAM activation has also had conflicting reports. Originally shown to bind only one SAM molecule per monomer, more recent ITC studies suggested a two-site model where a kinetically stabilizing high-affinity SAM binding site would be formed from oligomerization, while enzyme activation is driven by SAM binding to the lower affinity S2 site observed in dimeric CBS Δ516-525 crystal structures 11,12,37 . Our cryo-EM structure of SAM-bound activated state (Fig. 2), mutagenesis data (Fig. 3), and previous biophysical analyses 10 all conform to the notion that only the S2 site exists to bind SAM. Though our ITC analysis of full-length CBS fits the two-site model (Fig. 3c, Extended Data Fig.  6), we reason that the thermograph reflects not only SAM binding but also the structural rearrangements that have to occur for activation. This transition from basal to activated states requires a significant conformational change and likely follows a multistep process (Extended Data Fig. 5d, Movie 2). Conformational changes due to ligand binding are known to be a major contributor to heat capacity changes 38 and there is precedence for ligand binding to Bateman modules to diverge from a simple one-site binding model when dimerization of Bateman modules occurs 39 . Therefore, we regard our data as relative measurements of both SAM binding and conformational changes. As the kinetically stabilising site has been suggested for drug discovery 11,37 , our findings here suggest that alternative frameworks in the context of filament should be considered for targeting the CBS regulatory domain (discussed below).
This study now firmly places human CBS in the growing membership of filamentous metabolic enzymes (Fig. 5a). Higher order oligomerization in response to signal transduction from ligand (nutrient) binding or stress has been shown for many eukaryotic metabolic enzymes such as acetyl-CoA carboxylase (ACC), inosine-5′-monophosphate dehydrogenase (IMPDH), and cytidine triphosphate synthase (CTPS) 32,33 . The yeast CBS orthologue, S. cerevisiae Cys4p, forms punctate foci during stationary phase in response to nutrient levels 40 , an observation that suggests filamentation 33 . However yeast Cys4p, contrary to human CBS, does not undergo allosteric feedback activation in response to SAM 6 and does not contain the same oligomerization loop in the regulatory domain (Extended Data Fig 8). Therefore, it remains unclear if SAM constitutes the signal or driver for Cys4p oligomerization. For human CBS, however, filament formation takes place both in the absence and presence of SAM. AlphaFold predictions 41 and sequence alignment of Bateman modules from various CBS orthologues suggests that filament formation is possibly conserved in chordates (Extended Data Fig. 8, 9). This therefore implies that CBS oligomerization could be an evolutionarily strategy overall but could involve different structural components and serve different functional outcomes.
For many metabolic enzymes, filamentation and oligomerization serve to provide new ligand binding sites, generate unique catalytic conformations, or transduce signals across multiple enzyme subunits. Such functional modification to the enzyme is often reflected in a significant increase (or decrease) in cooperativity and activity upon filament formation 32,33 . For the case of human CBS, we observe only a modest increase in cooperativity in comparison to the loop deleted CBS Δ516-525 construct (Fig. 4a). This is not surprising as the CBS filament interface involves a single point of contact (Fig. 1, 2). In other enzymes, such as IMPDH which forms a filament of tetramers, multiple contacts are formed across single filament interfaces with corresponding high values of cooperativity 42 . We do however find that the full-length CBS filament is more stable and less prone to thermal activation than the loop-deleted CBS Δ516-525 dimer (Fig. 4b, c). We previously observed that the CBS Δ516-525 construct is conformationally flexible without SAM, presenting as two populations in ion mobility experiments 10 . Thus, we propose that the primary objective of filament formation in CBS is to increase the kinetic stability of the regulatory domain to maintain the basal conformation of the enzyme 11,31,37 (Fig.  5a). The notion of filament formation increasing stability is further supported by the His-tagged construct that presents longer polymers, higher stability, and less degradation than the construct without a His-tag (Fig. 4b, Extended Data Fig. 2). Increased stability and activity of human CBS due to a C-terminal His-tag has been previously reported 30 . Unfortunately, we cannot structurally rationalize this effect as we observed no interpretable density in the maps of this construct for the affinity tag at the Bateman-Bateman interface (Fig. 1, 2). We theorise though that the His-tag could be acting as a proxy for an as yet unidentified ligand that may regulate CBS oligomerization. Further investigations are clearly warranted; however, these observations show that filament formation can be modulated (positively or negatively) by changes at the Bateman-Bateman interface.
Inherited mutations in CBS result in classical homocystinuria (HCU), in which most recorded mutations are missense 4 , and the dominant molecular mechanisms have been recognised as protein misfolding and aggregation 17,19,20 (Fig. 5b). Rescue of mutant CBS activity has been documented by chemical chaperones 35,43 , heme arginate 44 , and proteostasis inhibitors 45 , suggesting a small molecule therapy could be developed 46,47 . It is intriguing that genetic suppression in a yeast model of the disease has also been reported, where deletion 29 or missense mutations on the regulatory domain 29 can overcome the deleterious effects of the most common HCU mutations. Disease associated mutants in general can produce hydrophobic patches in the protein due to local misfolding, that will result in aggregation 48-50 . It is probable that many HCU mutations generate hydrophobic patches on the catalytic domain resulting in further non-specific interactions that lead to aggregation 19 (Fig. 5b).
Considering our findings, we hypothesise that a mechanism of rescue could be the reduction of the natural propensity for CBS to polymerise which could reduce one pathway towards aggregation (Fig. 5d). In support of our reasoning, 1) deletion of the regulatory domain prevents filament formation (Extended Data Fig. 2), and 2) the seven reported suppressor mutations from the yeast model of disease can be all mapped onto the hydrophobic face of the regulatory domain that forms the Bateman-Bateman interface (Fig. 5c, Extended Data Fig.  10a). All seven residues are conserved in chordate CBS (Extended Data Fig. 8) and are predicted to alter interactions at the oligomeric interface (Extended Data Fig 10b). The original report suggested that these mutants altered the interaction between the regulatory and catalytic domains trapping CBS in a partially open conformation which is non-responsive to SAM. However, in the background of the wild-type enzyme no slight increase in basal activity was observed 28 and as such we believe that altered oligomerization should be considered as an aspect of rescue. As dimeric CBS Δ516-525 behaves almost like full-length (i.e., is active and SAM responsive), a small molecule that disrupts CBS polymerization and reduces aggregation could be a potential therapeutic avenue for the treatment of HCU (Fig 5d).
Overall, we have determined multiple structures of human CBS showing that the fulllength enzyme polymerises as an active filament which changes conformation due to SAM. Future work should consider further the role of CBS polymerization in protein misfolding and aggregation. It is interesting that there are catalytic domain HCU mutations that result in a CBS enzyme with normal basal activity but non-responsive to SAM 43 . SAM non-responsive HCU mutations in the regulatory domain exhibited an enzymatic activity closer to the activated state 34 , suggesting that some mutants may lock CBS in one conformation. Cryo-EM studies of these and other disease associated mutants will give insight into the molecular mechanism of protein misfolding of CBS and may have implications in understanding the misfolding of other multidomain metabolic enzymes.

Cloning, expression, and purification of human CBS proteins.
The gene for human CBS (UniProt P35520) was cloned into pNIC-Bsa4 and pNIC-CH encoding for a TEV cleavable Nterminal and permanent C-terminal His-tag respectively. The constructs CBS Δ516-525 and CBS CD (residues 1-413) along with single point mutations of CBS were introduced using In-Fusion (Takara) or QuikChange (Agilent) mutagenesis and confirmed by sequencing. CBS was expressed in E. coli Rosetta (DE3) cells in auto induction Terrific Broth (TB) supplemented with 50 μg/ml kanamycin, 34 μg/ml chloroamphenicol, 0.3 mM δ-aminolevulinic acid, 0.0025% pyridoxine-HCl, 0.001% thiamine-HCl, and 0.1 mM ferric chloride at 30 °C, 200 rpm for 24 hours. Cells were resuspended in lysis buffer (50 mM sodium phosphate, pH 7.5, 500 mM NaCl, 0.5 mM TCEP, 5% glycerol, 1.0% Triton X-100, 0.1 mM PLP, 2 mg/ml lysozyme) and lysed by sonication. CBS proteins with a TEV cleavable N-terminal His-tag were purified using Ni-NTA agarose (Qiagen) resin and were treated to gel filtration using a Superose 6 Increase 16/600 column or Superdex 200 Hiload 16/600 column (Cytiva) equilibrated in storage buffer (25 mM HEPES, pH 7.5, 500 mM NaCl, 0.5 mM TCEP, 5% glycerol). Fractions containing CBS protein were pooled and treated with His-tagged TEV protease overnight at 4 °C, and then passed over Ni-NTA agarose resin to remove the TEV protease and uncleaved protein. Movies of the CBS FL-CHis basal state were collected at eBIC (Diamond Light Source) on a Titan Krios equipped with a Falcon 3EC direct electron detector (Thermo Fisher Scientific) operating in counting mode. Images were imaged at 300 kV with a magnification of 75,000×, corresponding to a pixel size of 1.085 Å. 40 frames over 60 seconds were recorded with a defocus range of -0.9 µm to -3.0 µm with a total dose of 37.85 e -A -2 (0.823 e -A -2 per frame). A total of 1,740 movies were collected in a single session. MotionCor2 51 was used to correct beam induced motion and CTF was estimated using CTFFIND-4.1 52 . For helical reconstruction, particles were picked using the filament picker of Relion 3.0.8 53 resulting in 239,739 particles extracted. Helical picks were subjected to multiple rounds of 2D classification producing 82,810 particles that were imported to CryoSPARC-3.1.0 54 . Further 2D classification to remove any junk particles reduced this to 76,663 particles. Helical parameters were roughly determined from a low resolution Glacios collected map. Nonuniform helical refinement with D1 symmetry (C2 symmetry perpendicular to the helical axis) imposed resulted in 3.7 Å map with refined helical twist of -108.4 º and rise of 51.2 Å. For single particle analysis, particles were auto-picked using the Relion 3.0.8 53 (Laplacian of Gaussian function) resulting in 760,869 particles extracted. One round of 3D classification with 4x binned images and a model from a subset of the data was used to remove bad particles and contamination. This resulted in 392,163 particles that were unbinned and subjected to per particle CTF refinement and Bayesian polishing. After another round of masked 3D classification, one class consisting of 207,509 particles was identified to have the highest level of structural detail. A further round of CTF refinement and Bayesian polishing followed by masked auto-refining was used to produce particles for cryoSPARC-3.1.0 54 . 2D classification followed by heterogonous refinement reduced the number of good particles to 188,230. Multiple rounds of non-uniform refinement, local CTF refinement and local non-uniform refinement with C2 symmetry imposed resulted in a 3.0 Å map.
EER formatted movies of the CBS FL basal state were collected at the York Structural Biology Laboratory (YSBL) on a Glacios equipped with a Falcon 4 direct electron detector (Thermo Fisher Scientific). Images were imaged at 200 kV with a magnification of 150,000×, corresponding to a pixel size of 0.935 Å. Movies over 5.18 seconds were recorded with a defocus range of -1.4 µm to -2.0 µm with a total dose of 50 e -A -2 . A total of 2,628 movies were collected in a single session. All movies were imported into cryoSPARC-3.3.2 54 where they subjected to patch CTF estimation and patch motion correction. For helical reconstruction, particles were picked using the filament tracer resulting in 749,213 particles extracted. Multiple rounds of 2D classification to remove any junk particles reduced this to 98,993 particles. Particle curation based off CTF fit further reduced this to 89,761 particles. Initial helical parameters were determined from the CBS FL-CHis map. Non-uniform helical refinement with D1 symmetry imposed resulted in 3.9 Å map with refined helical twist of -108 º and rise of 51 Å. For single particle analysis, 1,190,611 particles were picked and extracted using template-based picking. Rounds of 2D classification resulted in 160,400 particles that were subjected to ab-initio reconstruction and heterogenous refinement with three classes. Two classes were further separately processed using local non-uniform refinement with C2 symmetry imposed resulted in a 3.8 Å maps of both degraded and non-degraded CBS.
Movies of the CBS FL-CHis activated state (SAM bound) were collected at eBIC (Diamond Light Source) on a Titan Krios (Thermo Fisher Scientific) equipped with a K3 (Gatan) direct electron detector operating in super-resolution mode. Images were imaged at 300 kV with a magnification of 81,000×, corresponding to a pixel size of 0.53 Å. 44 frames over 3.53 seconds were recorded with a defocus range of -0.9 µm to -3.0 µm with a total dose of (0.908 e -A -2 per frame). 11,220 movies were collected in a single session. All movies were imported into cryoSPARC-3.1.0 54 where they were motion corrected and the CTF estimated using patch motion correction (Fourier cropped to 1.06 Å) and patch CTF estimation respectively. Processing the activated state took considerable effort and initially filaments were picked using the filament tracer without templates on 2,790 micrographs. The resulting best classes from 2D classification were then used for another round of filament picking. Another round of 2D classification and picking the best classes were used to produce templates representative of the two dominant views with different filament widths. Two separate rounds of filament picking on the entire dataset resulted in 2,374,969 and 2,865,445 particles, which were eventually merged into a pool of 492,224 particles after many rounds of 2D classification and removal of duplicate particles. Helical parameters were roughly determined by visual inspection of a low resolution Glacios collected map. Rounds of non-uniform helical refinement with D1 symmetry imposed were used to re-centre particles and remove duplicates within 44 Å resulting in 425,260 particles. One further round of non-uniform helical refinement with D1 symmetry imposed resulted in a map at 4.0 Å resolution of the full filament with a refined helical twist of -178.6º and rise of 46.7 Å. Subsequently this map was used to make a soft mask (10 Å dilation with a soft padding of 50 Å) of the central filament region. Imposing this as a static mask during non-uniform helical refinement with D1 symmetry imposed resulted in a 4.1 Å resolution of the central regulatory domain with a helical twist of -177.7 º and rise of 47.2 Å. To improve the resolution of the central regulatory domain the particles were then subjected to a masked local refinement with D1 symmetry applied and a less soft central regulatory domain mask (10 Å dilation with a soft padding of 20 Å). This resulted in a map with a resolution of 4.1 Å. Though distortions due to the flexibility of this central region were apparent at the edges of the map the three dimeric repeats at the centre of the map had improved features. To improve the quality and resolution of the highly flexible catalytic domains, masked local refinement with D1 symmetry imposed with a soft mask of the most central catalytic and regulatory domains (6 Å dilation with a soft padding of 20 Å) was used. Here the global helical map was filtered to 20 Å and alignments only considered a resolution of up to 9 Å resulting in map of 8.3 Å resolution.
Model fitting, refinement, and validation. For the CBS FL basal state structures, initially three CBS Δ516-525 structures (PDB: 4COO) were fitted using Molrep 55 and the missing loop 513-527 was manually built in Coot 56 . Multiple copies of the CBS FL model were docked into each map as appropriate using Phenix 57 . Rounds of refinement in Phenix 57 were then used to refine the structure with manual adjustments in Coot 56 . For the activated state multiple copies of the isolated Bateman domain from our basal structure was docked using Phenix 57 into the central locally refined map, and then flexibly fitted into a 10 Å filtered map using Namdinator 58 . This was followed by a second round of flexible fitting using the non-filtered map. The crystal structure of the Bateman loop-deleted dimer bound to SAM (PDB: 4UUU) was used as a guide to dock SAM into the appropriate density. This model and our basal state model were then used as references for refinement of the entire SAM bound model using Isolde 59 and Phenix 57 . For the 8.3 Å map of a single catalytic domain the CBS CD structure (PDB: 4PCU) was manually fitted into the density using Chimera 60 . These models were then assembled into a pseudoatomic model of the global 4.1 Å activated map. All models were validated using Molprobity 61 .
Enzyme activity assay. Kinetic parameters were determined by monitoring hydrogen sulphide (H2S) production using the fluorescent probe 7-azido-4-methylcoumarin (AzMC) 62 . Assays were performed in 25 mM HEPES, pH 7.5, 200 mM NaCl, 5 μM PLP, 10 mM glutathione, 10 μM AzMC, with 0.01% triton-x 100, in 384 well black plates, as a final assay volume of 50 µl. A final concentration of 100 nM of each CBS construct was used. For Michaelis-Menten kinetics cysteine was varied 0-40 mM with a constant 10 mM homocysteine and homocysteine varied 0-10 mM with a constant 40 mM cysteine. 300 µM SAM was added when appropriate. SAM titration assays were performed with a final concentration of 10 mM homocysteine and 40 mM cysteine, and SAM was added at a range of 0-1.0 mM. Thermal activation was carried out with CBS protein at 1 µM in 25 mM HEPES, pH 7.5, 200 mM NaCl, 50 μM PLP as 50 µl aliquots treated at different temperatures using a VeritiPro thermal cycler (Thermo Fisher Scientific) for two minutes. Treated samples were then put into ice before activity was assayed with 10 mM homocysteine and 40 mM cysteine. All plates were preincubated with enzyme for 10 minutes at 37 ºC before the addition of cysteine. Plates were sealed with and spun at 900 x g for one minute before loading into the plate reader. H2S production was monitored by fluorescence at 450 nm (λex = 365 nm) using a OmegaSTAR (BMG Biotech) at 37 ºC. Each plate was read for one hour with a reading every one minute and raw rates were determined using MARS software (BMG Biotech). Activity readings were calibrated using a standard curve of known H2S concentrations using sodium hydrosulfide hydrate as a H2S source. Kinetic analyses were done in GraphPad Prism.
Thermal shift assay. CBS constructs were diluted in thermal shift buffer (25 mM HEPES, pH 7.5, 200 mM NaCl, 2.0 mM TCEP) to 0.3 mg/ml with SYPRO-Orange (Invitrogen) diluted 1000X in a total volume of 20 μl. A QuantStudio 3 RT-PCR machine (Thermo Fisher Scientific) was used to measure melting temperatures.
Isothermal titration calorimetry. Purified CBS proteins were buffer exchanged into 20 mM HEPES, pH 7.4 using Zeba spin columns (Thermo Fisher Scientific) at 4 °C. To prevent precipitation CBS FL-CHis and its mutants were buffer exchanged into 20 mM HEPES, pH 7.4, 0.01% triton X-100 whereas CBS RD was exchanged into 20 mM HEPES, pH 7.4, 200 mM NaCl. The appropriate buffer was then used to dissolve SAM from stocks to 500 µM. A MicroCal PEAQ-ITC machine with v1.21 control software for data collection (Malvern Panalytical) was used to perform ITC. CBS constructs were tested at 30-60 µM monomer in a 200 µl sample cell and were injected with 0.4 µl followed by 44 x 0.8 µl of SAM with 150 s spacing at 25 °C. Heats of dilution were determined by separate runs of SAM injected into buffer alone. Integrated heats were fit to using the Microcal PEAQ-ITC analysis software v1.30 (Malvern Panalytical) to obtain n, Kd, ∆H, and -T∆S.
Structural analysis using AlphaFold multimer. CBS sequences were obtained from UniProt and their sequences aligned using Clustal Omega 63 . AlphaFold2 multimer 64 was used through the implementation in ChimeraX 60 . Six copies of the selected CBS Bateman domains were used as the input and the top scored model was used for structural analysis. All lower scored models were essentially identical to the top scorer for all orthologues.    Extended Data Fig. 9 | AlphaFold predicts SAM responsive CBS enzymes polymerise as filaments. a, AlphaFold prediction using six copies of the human CBS regulatory domain (residues 408-551) shows a filament architecture identical to the cryo-EM model of the activated state. b, AlphaFold prediction using six copies of the mouse CBS regulatory domain (residues 404-561) shows a filament architecture similar to the cryo-EM model of the human CBS activated state. c, AlphaFold prediction using six copies of the bovine CBS regulatory domain (residues 410-571) shows a filament architecture similar to the cryo-EM model of the human CBS activated state. d, AlphaFold prediction using six copies of the African clawed frog CBS regulatory domain (residues 401-562) shows a filament architecture similar to the cryo-EM model of the human CBS activated state. e, Structural alignment of the Bateman-Bateman interface from the AlphaFold predicted structures of human, mouse, bovine and frog CBS.  n/a n/a n/a n/a n/a n/a