Structural basis for the inhibition of the Bacillus subtilis c-di-AMP cyclase CdaA by the phosphoglucomutase GlmM

Cyclic-di-adenosine monophosphate (c-di-AMP) is an important nucleotide signaling molecule that plays a key role in osmotic regulation in bacteria. c-di-AMP is produced from two molecules of ATP by proteins containing a diadenylate cyclase (DAC) domain. In Bacillus subtilis, the main c-di-AMP cyclase, CdaA, is a membrane-linked cyclase with an N-terminal transmembrane domain followed by the cytoplasmic DAC domain. As both high and low levels of c-di-AMP have a negative impact on bacterial growth, the cellular levels of this signaling nucleotide are tightly regulated. Here we investigated how the activity of the B. subtilis CdaA is regulated by the phosphoglucomutase GlmM, which has been shown to interact with the c-di-AMP cyclase. Using the soluble B. subtilis CdaACD catalytic domain and purified full-length GlmM or the GlmMF369 variant lacking the C-terminal flexible domain 4, we show that the cyclase and phosphoglucomutase form a stable complex in vitro and that GlmM is a potent cyclase inhibitor. We determined the crystal structure of the individual B. subtilis CdaACD and GlmM homodimers and of the CdaACD:GlmMF369 complex. In the complex structure, a CdaACD dimer is bound to a GlmMF369 dimer in such a manner that GlmM blocks the oligomerization of CdaACD and formation of active head-to-head cyclase oligomers, thus suggesting a mechanism by which GlmM acts as a cyclase inhibitor. As the amino acids at the CdaACD:GlmM interphase are conserved, we propose that the observed mechanism of inhibition of CdaA by GlmM may also be conserved among Firmicutes.

important function in regulating cell size, either directly or indirectly through its function in osmotic regulation, cell-wall integrity, and susceptibility to beta-lactam antibiotics, which target the synthesis of the peptidoglycan cell wall (9)(10)(11)(12).
The function of c-di-AMP has been most extensively studied in a range of Firmicutes bacteria including the Grampositive model organism Bacillus subtilis and Gram-positive bacterial pathogens such as Staphylococcus aureus, Listeria monocytogenes, and several Streptococcus species (9,10,(13)(14)(15)(16)(17). From these studies, it has become apparent that the cellular level of c-di-AMP needs to be tightly regulated as both an excess and a lack of c-di-AMP can negatively impact bacterial growth, physiology, and virulence (17,18). To achieve the optimal level, a dynamic equilibrium must exist between the synthesis of c-di-AMP via diadenylate cyclases (DACs) and its degradation into 5 0 -phosphadenylyl-adenosine (pApA) or two molecules of AMP by phosphodiesterases (18)(19)(20). As part of the current study, we investigated how the activity the B. subtilis c-di-AMP cyclase CdaA is regulated by GlmM, a phosphoglucomutase enzyme required for the synthesis of an essential peptidoglycan precursor.
c-di-AMP is formed from two molecules of ATP by enzymes containing a DAC domain. These enzymes have been extensively characterized structurally as well as biochemically, but how their activity is regulated is an aspect that remains poorly understood. B. subtilis codes for three DAC enzymes (3,(21)(22)(23)(24). CdaA (also referred to as DacA in some bacteria) is a membrane-bound cyclase with three predicted N-terminal transmembrane helices and a cytoplasmic catalytic DAC domain. CdaA (DacA) is the "housekeeping" c-di-AMP cyclase in Firmicutes, as it is conserved and often the sole c-di-AMP cyclase in this phylum (25,26). The two other B. subtilis c-di-AMP cyclases, DisA and CdaS, are soluble proteins, not as widely distributed among bacteria and have more specialized functions, with DisA involved in controlling DNA-repair processes during sporulation or spore outgrowth and CdaS also specifically expressed during the sporulation process (22,23,27). While there are no publications on the 3D-structures of the B. subtilis c-di-AMP cyclases, structures are available for the cytoplasmic enzymatic domains of the L. monocytogenes and S. aureus CdaA/DacA homologs (21,28), the DisA homolog from Thermotoga maritima (3), and the CdaS homolog from Bacillus cereus (PDB 2FB5). These studies revealed that DAC domains have a mixed αß-fold, with highly conserved DGA and RHR amino acid motifs required for ligand binding (3,21,29). Formation of c-di-AMP requires a head-to-head conformation of two DAC domains. This was first demonstrated in the crystal structure of DisA, a protein that forms an octamer with four DAC domain dimers in the active head-tohead conformation (3). While the L. monocytogenes and S. aureus CdaA/DacA catalytic domains and the CdaS protein, were also present as dimers and hexamers, respectively, they were in an inactive conformation. These proteins therefore either need to rearrange or more likely form higher oligomers in order to yield active enzymes with DAC domains in the head-to-head dimer conformation (24,28). Recently, another structure of the cytoplasmic catalytic domain of the L. monocytogenes CdaA enzyme (Δ100CdaA) has been reported with a c-di-AMP bound between two monomers, which based on the crystal cell packing were arranged in an active dimer of dimer configuration (30). These findings are consistent with the idea that CdaA (DacA) enzymes will need to form higher oligomers to achieve an active enzyme configuration. Hence, factors influencing the ability of c-di-AMP cyclases to rearrange into an active conformation or to form higher oligomers will be able to regulate the activity of these enzymes.
The genetic arrangement and operon structure coding for the "housekeeping" c-di-AMP cyclase CdaA (DacA) is conserved in Firmicutes (29,31). Two genes, coding for the membrane-linked CdaA regulator CdaR (also named YbbR in some bacteria) and cytoplasmically located peptidoglycan precursor synthesis enzyme GlmM, are found downstream and in an operon with cdaA (29,31). Through recent studies in B. subtilis, L. monocytogenes, Lactococcus lactis, and S. aureus, it is has become apparent that these three genes are not only cotranscribed but that the encoded proteins also form a complex and that CdaR and GlmM can regulate the activity of the c-di-AMP cyclase CdaA (29,32,33). While CdaR has been reported to function as both an activator and a repressor of CdaA depending on the growth conditions, GlmM has been shown to be a potent inhibitor of the cyclase (17,29,31,32,34). However, the molecular mechanisms on how the CdaA cyclase activity is regulated by these proteins are not yet known, and this was further investigated as part of this study.
GlmM is a phosphoglucomutase enzyme catalyzing the conversion of glucosamine-6-phosphate to glucosamine-1phosphate, which is subsequently used to produce the essential peptidoglycan precursor UDP-N-acetyl-glucosamine (35). In B. subtilis, L. monocytogenes, and L. lactis, a protein-protein interaction between CdaA and GlmM has been detected using bacterial two-hybrid assays performed in Escherichia coli (29,31,33). In B. subtilis this interaction has been further confirmed by in vivo protein cross-linking and pull-down assays (29) and in L. monocytogenes by the coelution of purified proteins (33). The first evidence that GlmM serves as negative regulator of CdaA/DacA activity came from an L. lactis strain that produces a GlmM variant that is thought to form a stronger interaction with CdaA; this strain produces lower cellular c-di-AMP levels than the bacteria expressing wild-type GlmM (31). Furthermore, the activity of the soluble recombinant S. aureus DacA catalytic domain (DacA CD ) could be blocked almost completely by the addition of purified GlmM protein in in vitro assays, and the recombinant proteins were shown to form a stable complex that could be purified via sizeexclusion chromatography (28). On the other hand, the activity of GlmM was not affected by the interaction with DacA CD (28). Additional mass spectrometry and small-angle X-ray scattering (SAXS) analyses suggested that the complex is composed of a DacA CD dimer and a GlmM dimer (28). Crystal structures of the individual S. aureus DacA CD and GlmM dimers revealed that the S. aureus DacA CD protein assumed an "inactive" dimer conformation. GlmM had the typical four-domain fold of phosphoglucomutases with a flexible C-terminal domain 4 and the dimer was "M-shaped," characteristic for this class of enzymes (28). However, a highresolution structure of the complex could not be obtained, and only a model for the complex could be proposed by fitting the individual DacA CD and GlmM dimer structures into the SAXS envelope (28). Based on this, a model was proposed in which GlmM could potentially block the activity of the DacA CD cyclase by preventing the formation of higher oligomers.
Here, we set out to provide atomic resolution information on the CdaA:GlmM complex to gain insight into the molecular mechanism of how GlmM can control the activity of the c-di-AMP cyclase enzyme. Using the purified B. subtilis CdaA catalytic domain (CdaA CD ) and purified full-length GlmM or the truncated GlmM F369 variant lacking the flexible C-terminal domain 4, we show that the two proteins form a stable complex in vitro and that GlmM and GlmM F369 are potent inhibits of the cyclase. Crystal structures of the B. subtilis CdaA CD cyclase, the GlmM phosphoglucomutase, and the CdaA CD :GlmM F369 complex were obtained, revealing dimer conformations of the individual proteins as well as a dimer of dimer conformation in the complex structure. More importantly, from the complex structure the mechanism by which binding of GlmM inhibits the cyclase activity becomes apparent, that is by preventing the oligomerization of CdaA and formation of active head-to-head cyclase oligomers.

Results
The B. subtilis phosphoglucosamine GlmM interacts with and inhibits the activity of the c-di-AMP cyclase CdaA CD Using the purified S. aureus DacA CD catalytic domain and GlmM, it has been shown that the proteins form a stable complex in vitro and that GlmM is a potent inhibitor of the cdi-AMP cyclase without requiring any additional factors (28). To examine if this is also the case for the Bacillus sutbilis proteins, the full-length B. subtilis GlmM protein and the truncated GlmM F369 variant were expressed and purified along with the soluble catalytic domain of the B. subtilis c-di-AMP cyclase CdaA CD . The GlmM F369 variant lacks the flexible C-terminal domain 4 and was constructed to aid subsequent structural investigations. The proteins were expressed as Histagged proteins in E. coli and purified individually via Ni-NTA affinity chromatography followed by size-exclusion chromatography (Fig. 1). To test for a CdaA-GlmM interaction, lysates of strains producing CdaA CD and GlmM (Fig. 1A) or CdaA CD and GlmM F369 (Fig. 1B) were mixed prior to affinity and sizeexclusion chromatography. The elution profiles and analysis of the retention volumes revealed that CdaA CD formed a complex with GlmM and with GlmM F369 that eluted as a single, highermobility species compared with the individual proteins (Fig. 1). The peak fractions of each complex were further analyzed by SDS-PAGE, confirming the presence of both proteins (Fig. 1, inserts). We also determined the binding affinity between GlmM and CdaA CD by microscale thermophoresis (MST). For the MST experiments, increasing concentrations of unlabeled purified GlmM ranging from a final concentration of 0.78 μM to 800 μM were mixed with fluorescence labeled CdaA CD held at a constant final concentration of 25 nM (see Experimental procedures sections for details). Based on the thermophoresis and normalized fluorescence change of CdaA CD depending on the GlmM protein concentration, a K d of 14.4 μM ± 0.962 was determined (Fig. 1C) indicating a moderate binding affinity. Next, to determine if the B. subtilis GlmM protein impacts the activity of CdaA CD , in vitro cyclase activity assays were performed, and the conversion of ATP (spiked with a small amount of α-32 P -labeled ATP) into c-di-AMP assessed. The purified B. subtilis CdaA CD protein was enzymatically active in the presence of the divalent metal ion Mn 2+ but showed only limited activity in the presence of Co 2+ or Mg 2+ ( Fig. 2A) and after 4 h incubation approximately 50% of the ATP substrate was converted to c-di-AMP (Fig. 2B). Addition of GlmM or GlmM F369 at a 2:1 M ratio over CdaA CD led to a significant reduction in the conversion of ATP to c-di-AMP (Fig. 2C). Taken together, these data show that the purified B. subtilis CdaA CD :GlmM and CdaA CD :GlmM F369 proteins form a stable complex in vitro and that the full-length and truncated GlmM variants inhibit the activity of the c-di-AMP cyclase CdaA CD .

Crystal structures of the B. subtilis CdaA CD and GlmM proteins
To gain atomic level details of the CdaA CD and GlmM protein complex, we started off by determining the crystal structures of the individual proteins. The tag-less B. subtilis CdaA CD protein was crystallized and the structure solved at 2.8 Å (Table 1 and Fig. 3). The protein displayed the expected DAC protein fold, with a central β-sheet made up of six antiparallel strands flanked by five helices (Fig. 3A). However, it lacked the seventh β strand that was seen in the structures of CdaA homologs of other bacteria (21,28). In B. subtilis CdaA CD the residues corresponding to this β-strand are instead in a loop that adapts a very similar confirmation to the β strand observed in other CdaA structures. Superposition of the B. subtilis CdaA CD structure with the L. monocytogenes Δ100CdaA (PDB 4RV7; sequence identity of the full-length proteins is 65%) (21) and S. aureus DacA CD (PDB 6GYW; sequence identity of the full-length proteins is 53%) (28) structures, all lacking the N-terminal transmembrane helices, gave r.m.s.ds of 0.79 and 0.75, respectively, highlighting the overall structural similarities of these enzymes (Fig. 3B). The B. subtilis CdaA CD structure was solved as a dimer in the asymmetric unit with hydrogen-bonding interactions observed at the interaction interface (Fig. 3C). Interactions were observed between the side chains of amino acid residues Asn166, Thr172, and Leu174 (site 1) and residues Leu150, Lys153, and Met155 (site 2) (Fig. 3C). Similar hydrogenbonding interactions were also identified in the S. aureus DacA CD and L. monocytogenes Δ100CdaA structures with amino acid residues in site 1 being absolutely conserved (28,30) (Fig. S1). Analysis of the interface with PDBePISA (36) indicated a buried surface of 1400 Å 2 , which is similar to the value of 1460 Å 2 previously reported for the S. aureus DacA CD protein, indicative of a stable dimer formation. In this dimer confirmation, the active sites face opposite directions and hence cannot be engaged in a catalytically active head-to-head conformation (Fig. 3A). Taken together, these data indicate that the conformationally inactive dimerization interface is conserved among different CdaA homologs in Gram-positive bacteria and that the enzyme needs to form higher oligomers for catalysis.
The His-tagged B. subtilis GlmM protein was crystallized and the structure solved by molecular replacement using the Bacillus anthracis GlmM structure (PDB 3PDK; (37)) as the search model (Table 1 and Fig. 3D). The B. subtilis GlmM protein displayed a four-domain architecture typical for phosphoglucosamine mutase proteins (28,37) (Fig. 3D). Domains 1 to 3 are comprised of α-β mixed cores linked via a flexible loop to domain 4, which displays a three-stranded β sheet fold surrounded by two α-helices (Fig. 3D). While one GlmM molecule was present in the asymmetric unit, the typical "M-shaped" GlmM dimer arrangement was observed in the crystal cell packing (Fig. S2). Interactions were formed between domains 1, leading to the formation of a large groove a Refers to the highest resolution shell. b R free was computed same as R work, using a test set (5%) of randomly selected reflections that were omitted from the refinement.  (Table 1 and Fig. S2). One of the crystal structures was obtained with a divalent cation bound to the catalytic serine residue, which during catalysis is thought to be converted to a phosphoserine residue and the metal ion playing an important role during catalysis (Fig. S2). The exact type of metal ion could not be deduced due to the limitation of the structural resolution. However, we speculate that it is a magnesium ion, as magnesium was present in the crystallization conditions, and this metal ion is usually also bound in fully active enzymes. Furthermore, when a magnesium ion was modeled into the structure and analyzed using the program CheckMyMetal (38), a better fit was observed as compared with zinc or calcium ions, which could also fill the density. In the second structure, a phosphate molecule (PO 4 ) was bound to Arg419, located within a loop region in domain 4 ( To understand how GlmM interacts and inhibits CdaA, we next aimed to obtain the structure of the complex. Any crystals obtained for the B. subtilis CdaA CD :GlmM complex diffracted poorly. On the other hand, diffracting crystals were obtained for the CdaA CD :GlmM F369 complex, in which the GlmM protein lacks the flexible C-terminal domain 4. The crystals were obtained under two different conditions (see Experimental procedures section), and the structure of the CdaA CD :GlmM F369 complex could be solved at 3.6 Å (Complex 1) and at 4.2 Å (Complex 2) by molecular replacement using the B. subtilis CdaA CD and GlmM (dimer) structures as search models (  (Fig. S4A). Furthermore, in both complex structures, three complex molecules were obtained in the asymmetric unit and each complex was composed of a GlmM F369 dimer and a CdaA CD dimer in the inactive dimer configuration (Figs. 4 and S3). The three complexes obtained in the asymmetric unit were almost identical to each other, as indicated by the superposition r.m.s.d. of 0.15 to 0.20 Å for complex 1 (Fig. S4B) and of 0.15 to 0.16 Å for complex 2 (Fig. S4C). Since the obtained complex structures were basically identical, all further descriptions are based on the higher resolution complex 1 structure. In the complex, a CdaA CD dimer was positioned in the large groove at the top of the GlmM F369 dimer and formed interactions with domain 2 of GlmM (Fig. 4, A-C). The complex was asymmetric, with one of the CdaA CD monomers, CdaA CD (2) (shown in light blue in Fig. 4) placed in the center of the GlmM F369 groove and the other monomer, CdaA CD (1) (shown in dark blue in Fig. 4) projecting toward the solvent. Similarly, most of the interactions of the GlmM F369 dimer with the CdaA CD dimer were made by GlmM F369 (1) (shown in dark pink in Fig. 4). PDBePISA analysis revealed an average buried surface area of 996 Å 2 in the interface between GlmM F369 (1) and the CdaA CD dimer, which was stabilized by four hydrogen bond and four ionic bond interactions between GlmM F369 (1) and CdaA CD (1) and five hydrogen bond and three ionic bond interactions with CdaA CD (2) (Table S1 and Fig. S5). On the other hand, only an average 220.3 Å 2 surface area is occluded in GlmM F369 (2) (shown in light pink in Fig. 4). Based on the PDBePISA analysis, GlmM F369 (2) only formed two hydrogen bond interactions with the CdaA CD (2) monomer but no interaction with CdaA CD (1) (Table S1 and Fig. S5). A more detailed analysis of the interface showed that several interactions are made between two α-helices from domain 2 of GlmM F369 (1), α1 and α2, with the CdaA CD (1) and CdaA CD (2) monomers, respectively (Fig. 4, C and D). The main interactions in the complex were formed between three residues, D151, E154, and D194 of domain 2 in GlmM F369 (1) and residue R126 in each of the CdaA CD monomers. More specifically, ionic bonds were formed between residue D195 in GlmM F369 (1) and residue R126 in CdaA CD (2). In addition, salt bridges were formed between residues D151 and E154 in GlmM F369 (1) and residue R126 but this time from CdaA CD (1) (Fig. 4, C and D, Table S2 and Fig. S5). The data suggest that residue R126 in CdaA CD is potentially one of the most critical residues for complex formation, as it contributes to a number of ionic as well as hydrogen-bond interactions and even though the complex is asymmetric, it contributes to interactions in both CdaA CD monomers.

CdaA CD cannot form active oligomers in complex with GlmM
To gain insight of how GlmM inhibits the activity of the c-di-AMP cyclase, we inspected the location of the active sites of CdaA CD in the complex. The active site of DAC-domain enzymes is characterized by DGA and RHR motifs, corresponding to residues D 171 GA and R 203 HR in B. subtilis CdaA ( Fig. 5; areas highlighted in yellow and green in the CdaA CD monomers). The active site in CdaA CD (2) was completely occluded upon interaction with the GlmM F369 dimer (Fig. 5, dark blue CdaA CD monomer with active site region highlighted in yellow) but the active site in CdaA CD (1) appeared at least partially exposed ( Fig. 5; light blue CdaA CD monomer with active site region highlighted in green). For CdaA CD to produce c-di-AMP active head-to-head dimers need to be formed (3). The crystal structure of the L. monocytogenes Δ100CdaA cyclase was recently determined with a c-di-AMP molecule bound in the catalytic site and an active head-tohead dimer conformation seen in the crystal packing (30). Using the L. monocytogenes Δ100CdaA structure (PDB 6HVL) as model, an active B. subtilis CdaA CD dimer was modeled and superimposed on CdaA CD (1) in the complex structure (Fig. 5). Although the active site of the CdaA CD (1) was exposed and accessible in the complex with GlmM F369 , in an active dimer conformation, parts of the second CdaA CD molecule would collide and overlap with GlmM F369 , highlighting that also CdaA CD (1) cannot form active head-to-head oligomers in the complex (Fig. 5). Taken together, these data indicate that in the complex, the interaction of GlmM with CdaA CD will prevent the formation of functional DAC enzyme oligomers, which is essential for the formation of c-di-AMP. The crystal structure of the CdaA CD :GlmM F369 complex therefore in CdaA CD (2) (light blue protomer) are completely occluded in the complex and B, the active site (yellow residues) of CdaA CD (1) (dark blue protomer) remains partially exposed. However, the modeling of another CdaA CD protomer (in red) that forms an active dimer with CdaA CD (1) (dark blue protomer) results in protein-protein clashes with the GlmM F369 (1) monomer in the complex. The active CdaA CD dimer was modeled based on the L. monocytogenes Δ100CdaA (PDB 6HVL) structure (30). provides insight on an atomic level on the catalytic inhibition of the DAC CdaA CD by the phosphoglucosamine enzyme GlmM.
Small-angle X-ray scattering analysis of B. subtilis CdaA CD :GlmM complex To determine whether the full-length B. subtilis GlmM protein interacts with CdaA CD in a similar manner as observed for GlmM F369 , a structural characterization of the CdaA CD :GlmM complex was performed via small-angle X-ray scattering (SAXS). To this end, the individual purified B. subtilis CdaA CD and GlmM proteins as well as the purified CdaA CD :GlmM complex and as control the CdaA CD :GlmM F369 complex were passed over an analytical size-exclusion column, followed by continuous automated SAXS data collection throughout the run (Figs. 6 and S6, Table S2). For CdaA CD and GlmM, the reconstructed maps were consistent with the proteins forming dimers and the maps were a good fit for the B. subtilis CdaA CD dimer (Fig. 6A) and GlmM dimer (Fig. 6B) structures, respectively. The reconstructed map for the CdaA CD :GlmM complex (V c : 890.1, R g : 44.65 Å, and d max : 161 Å) was bigger in volume and dimensions as compared with the individual maps calculated for GlmM (V c : 625.8; R g : 37.29 Å, d max : 122 Å) and CdaA CD (V c : 373.2, R g : 26.94 Å, d max : 88 Å), which is consistent with the formation of a complex. From the Guinier plot analysis, the molecular weight of the B. subtilis CdaA CD :GlmM complex was calculated to be 130 kDa, which is consistent with the theoretical molecular weight of 144.46 kDa for a complex made of two CdaA CD and two GlmM molecules. To fit a CdaA CD :GlmM dimer complex into the reconstructed map, a model of the complex with full-length GlmM was first constructed by superimposing the crystal structure of full-length GlmM onto the CdaA CD :GlmM F369 complex structure. The resulting complex model was subsequently fitted in the reconstituted SAXS envelope of the complex. A good fit of the CdaA CD :GlmM dimer model complex into the reconstructed envelope was observed; however, an elongated density on one side remained unoccupied (Fig. 6C). It is plausible that the flexible C-terminal domain 4 of the GlmM protein is responsible for this extra density. As control, an SAXS experiment was also performed using the CdaA CD :GlmM F369 complex sample for which the X-ray structure was obtained. The dimensions of the CdaA CD :GlmM F369 complex were V c : 656.8, R g : 37.51 Å, and d max : 117.5 Å and the molecular weight was calculated to be 97.5 kDa, which is consistent with the theoretical molecular weight of 120 kDa for a complex made of two CdaA CD and two GlmM F369 molecules. Similarly, a good fit of the CdaA CD :GlmM F369 dimer complex structure was obtained when fitted into the reconstructed SAXS envelope data (Fig. 6D). These data suggest that the full-length GlmM protein likely forms a dimer-of-dimer complex with the c-di-AMP cyclase CdaA CD and might assume a similar arrangement as observed for the CdaA CD :GlmM F369 complex.
Arginine 126 in B. subtilis CdaA CD is essential for complex formation The complex structure highlighted key interactions between residues D194 and residues D151/E154 in GlmM with residue R126 in each of the CdaA CD monomers (Fig. 5D). To confirm our structural findings, a site-directed mutagenesis analysis was performed. To this end, D195A, D151A/E154A, and D151A/E154A/D191A alanine substitution GlmM variants were created. Furthermore, residue R126 in CdaA CD , which in both monomers makes contacts with GlmM, was mutated to an alanine. The different alanine substitution variants were expressed and purified from E. coli and complex formation assessed by size-exclusion chromatography. While our initial experiments using the GlmM single, double, and triple alanine substitution variants appeared not to or only marginally affect complex formation with CdaA CD (Fig. S7), no complexspecific peak was observed when the interaction between the CdaA CD -R126A variant and GlmM was assessed. Instead, two peaks were observed for the CdaA CD -R126A:GlmM sample, one corresponding to the retention volume of GlmM and the another to CdaA CD -R126A (Fig. 7A). Analysis of the elution fractions from the CdaA CD -R126A/GlmM sample by SDS-PAGE and Coomassie staining showed that only a very small fraction of the CdaA CD -R126A protein coeluted with GlmM (Fig. 7A). These data highlight that, consistent with the structural data, residue R126 in CdaA CD plays a key role for the complex formation with GlmM. Based on these data, it can be predicted that the cyclase activity of the CdaA CD -R126A variant should no longer be inhibited by GlmM. To test this experimentally, in vitro cyclase enzyme activity assays were performed. The CdaA CD -R126A variant was active, although the activity was reduced as compared with wild-type CdaA CD (Fig. 7B). Importantly and in contrast to wild-type CdaA CD , the enzyme activity of this variant was no longer inhibited by the addition of GlmM (Fig. 7B). These data show that residue Arg126 in B. subtilis CdaA CD plays a critical role for complex formation and that GlmM can only inhibit the activity of the c-di-AMP cyclase after the formation of a stable complex.

Discussion
In this study, we show that the B. subtilis GlmM and CdaA CD cyclase domain form a stable dimer-of-dimer complex. GlmM acts through this protein-protein interaction as a potent inhibitor of the c-di-AMP cyclase without requiring any additional factors. Based on the atomic-resolution complex structure data, we suggest that GlmM inhibits the activity of CdaA CD by preventing the formation of active head-to-head cyclase oligomers.
For CdaA to produce c-di-AMP, two monomers need to be arranged in an active head-to-head conformation. As part of this study, we determined the structure of the B. subtilis CdaA CD protein and show that it has the typical DAC domain fold. While the protein was also found as a dimer in the structure, the dimer was in an inactive conformation, with the two active sites facing in opposite directions. The interface creating the inactive dimer conformation is conserved among CdaA proteins. The L. monocytogenes and S. aureus homologs, for which structures are available, were found in the same inactive dimer conformation even though the proteins crystallized under different conditions and were found in different space groups (21,28,30). This makes it less likely that a crystallographic symmetry artifact is responsible for the observed inactive dimer configuration. In addition to the inactive dimer configuration within an asymmetric unit, an active dimer conformation was observed in the L. monocytogenes Δ100CdaA protein by inspecting adjacent symmetry units (30). However, no such active dimer head-tohead conformations were identified for the B. subtilis CdaA CD protein across different symmetry units in the current structure. While not further investigated as part of this study, previous work on the S. aureus homolog indicated that the inactive dimer conformation is very stable, and in order for the protein to produce an active enzyme, the protein needs to form higher-level oligomers (28). Given the similarity in the interaction interface, this is likely also the case for the B. subtilis CdaA CD enzyme, and we would suggest that the B. subtilis CdaA CD dimer observed in the structure is unlikely to rearrange into an active dimer conformation.
We also solved the structure of the B. subtilis GlmM enzyme. The protein assumed the typical 4-domain architecture previously reported for GlmM enzymes (28,37) and the "M shape" in the dimer conformation, which in the case of the Bacillus sutbtilis GlmM protein was formed across two adjacent crystallographic units. The B. subtilis GlmM structure further highlighted the flexibility of the most C-terminal domain 4, which was found in the most open conformation seen in any GlmM protein structure up to date. The conformational flexibility of domain 4 is probably also a main factor why we were unsuccessful in determining the structure of a complex between CdaA CD and full-length GlmM. However, GlmM domain 4 is not required for the interaction with and inhibition of CdaA CD , since a B. subtilis GlmM variant lacking domain 4 formed a complex and inhibited the activity of B. subtilis CdaA CD . Furthermore, by using the B. subtilis GlmM F369 variant lacking the flexible domain 4, we were able to obtain the structure of the CdaA CD :GlmM F369 complex, revealing for the first time structural details at the atomic level for this complex, thereby identifying the amino acids important for the interaction between the two proteins. Several electrostatic interactions were detected between CdaA CD :GlmM F369 between the negatively charged residues D151, E154, and D195 in domain 2 of B. subtilis GlmM F369 with the positively charged residue R126 in CdaA CD . We could further show that replacing residue R126 in CdaA CD with an alanine abolished complex formation and the activity of the CdaA CD -R126 variant was no longer inhibited by GlmM. A direct protein-protein interaction between CdaA and GlmM has now been reported for these proteins in several Firmicutes bacteria, and hence the amino acids required for the interaction might be conserved. Indeed, a ConSurf (39) analysis using 250 CdaA protein sequences showed that the residue corresponding to R126 in B. subtilis CdaA is conserved between the different homologs (Fig. S8). Likewise, all the three negatively charged residues, D151, E154, and D195 in GlmM, which mediate the primary electrostatic interactions with R126 of CdaA CD , are highly conserved (Fig. S8). In previous work, we have shown that the S. aureus DacA CD (the CdaA CD homolog) does not interact with GlmM proteins from E. coli and Pseudomonas aeruginosa, two Gram-negative bacteria (28). While negatively charged amino acids corresponding to residues E154 and D195 in B. subtilis GlmM are also found in the GlmM protein from the Gram-negative bacteria (D153 and E194 in E. coli and D152 and E193 in P. aeruginosa), the amino acids at the equivalent position of D151 in B. subtilis GlmM are an arginine residue (R150 in E. coli and R149 in P. aeruginosa), which may hinder the complex formation between CdaA (DacA), and GlmM proteins of Gram-negative bacteria (28).
In a previous work, we proposed a model whereby GlmM inhibits the activity of CdaA cyclase activity by preventing the formation of active head-to-head oligomers (28). In the absence of an actual atomic resolution structure of the complex, this model was based on SAXS envelope data and fitting individual protein structures. The model predicted that the likely interaction site between CdaA and GlmM proteins is domain 2 of GlmM (28). The structure of B. subtilis CdaA CD :GlmM F369 complex we present here now provides experimental evidence for such a model and shows that GlmM indeed inhibits the activity of the CdaA cyclase in vitro by preventing the formation of active head-to-head oligomers. The K d between CdaA CD and GlmM was in the μM range, which will likely allow complex formation and dissociation in response to changes in protein levels and/or changes in cellular or environmental conditions. GlmM is an essential metabolic enzyme required for the synthesis of the peptidoglycan precursor glucosamine-1-P and thought to be predominantly located within the cytoplasm of the cell (33). However, based on the work presented in this study and previous findings, it is assumed that under certain conditions, a fraction of GlmM will localize to the bacterial membrane and interact with and inhibit the activity of the membrane-linked c-di-AMP cyclase CdaA (DacA) (28,32,33). As a result of this interaction, cellular c-di-AMP levels would decrease and consequently potassium and osmolyte uptake will increase. Recent work on L. monocytogenes suggests that GlmM regulates CdaA during hyperosmotic stress conditions, as during these conditions, overexpression of GlmM has been shown to result in a decrease in cellular c-di-AMP levels (33). The resulting activation of potassium and osmolyte transporters due to a drop in cellular c-di-AMP levels will help cells to counteract the water loss under osmotic stress conditions and aid in bacterial survival. However, what exact cellular changes caused by the osmotic upshift lead to a relocalization of GlmM to the membrane to form a complex with CdaA is currently not known and will require further investigation.
The level of c-di-AMP is regulated by a fine balance between the activities of the cyclase, which synthesizes c-di-AMP, and the phosphodiesterases, which break it down. Interestingly, these two classes of enzyme appear to be regulated very differently; whereas the activity of several phosphodiesterases has been shown to be regulated by small molecules, cyclase activity appears to be regulated through protein-protein interaction. For example, the stringent response alarmone (p) ppGpp has been shown to inhibit the activity both GdpP and PgpH enzymes (11,20). Furthermore, binding of heme to the Per-ARNT-Sim (40) signaling domain in GdpP (which is separate from its DHH/DHHA1 enzymatic domain that is responsible for the degradation of c-di-AMP) was shown in in vitro enzyme assays to result in reduced phosphodiesterase activity (40). Interestingly, the ferrous form of heme bound to GdpP could form a pentacoordinate complex with nitric oxide (NO), resulting in increased c-di-AMP phosphodiesterase activity. Based on these data it has been suggested that GdpP is a heme or NO sensor, resulting in decreased or increased activity respectively (41). The function consequence and impact of (p)ppGpp, heme, or NO binding to the phosphodiesterases on bacterial physiology have not yet been fully investigated. However, from these data it is clear that the activity of the c-di-AMP phosphodiesterases can be regulated by small-molecule ligands.
On the other hand, several proteins have been found to interact with and regulate the activity of c-di-AMP cyclases. The B. subtilis DisA protein is involved in monitoring the genomic stability ensuring that damaged DNA is repaired before cells progress with the sporulation process or exit from spores (27,42). DisA is encoded in a multigene operon and the gene immediately upstream of disA codes for RadA (also referred to as SMS). B. subtilis RadA possesses 5 0 to 3 0 DNA helicase activity, contributes to DNA repair and DNA transformation processes in B. subtilis, and has been shown to interact and negatively impact the activity of DisA (27). However, the mechanistic basis of how RadA binding to DisA inhibits the cyclase is currently not known. There is now ample evidence that the activity of the "house-keeping" membrane-linked c-di-AMP cyclase CdaA is impacted by two interacting proteins, the membrane-linked regulator protein CdaR and the cytoplasmic phosphoglucomutase enzyme GlmM (29,33). We have provided experimental evidence for the mechanistic basis by which GlmM inhibits the activity of CdaA, that is, by preventing the formation of active higherlevel oligomers. How CdaR regulates the cyclase activity of CdaA remains unclear. Recent work on the homologous proteins in L. monocytogenes indicated that the interaction of CdaA with CdaR takes place via the N-terminal transmembrane region of CdaA and GlmM has been shown to interact directly with the cytoplasmic cyclase domain of CdaA in S. aureus (28,33). Here, we show that this is also the case for the B. subtilis GlmM protein, which can bind without the requirement of any additional factor to the catalytic CdaA CD domain. In future works, it will be interesting to determine the structure of the full-length CdaA enzyme, which might provide further insight into how the enzyme forms higher oligomers for activity as well as how it interacts with CdaR. Furthermore, it will be interesting to further investigate the interaction between GlmM and CdaR with CdaA within bacterial cells to determine if this interaction is dynamic and which stimuli will promote or prevent complex formation to fine-tune the synthesis of c-di-AMP. Identifying how interacting proteins regulate the activity of these cyclases will provide important insight of how bacterial cells maintain proper levels of c-di-AMP under different growth conditions and in different environments.

Bacterial strains and plasmid construction
All bacterial strains and primers used in this work are listed in Tables S3 and S4, respectively. pET28b-derived plasmids were constructed for the overproduction of the C-terminal catalytic domain of the B. subtilis CdaA enzyme starting from amino acid Phe97 and referred to as CdaA CD , GlmM, and the GlmM F369 variant comprising residues Met1 to Phe369 but lacking the C-terminal domain 4. To this end, the corresponding DNA fragments were amplified by PCR using B. subtilis strain 168 chromosomal DNA as template and primer pairs ANG2760/ANG2761 (cdaA CD ), ANG2762/ ANG2763 (glmM), and ANG2762/ANG2764 (glmM F369 ). The PCR products were purified, digested with NheI/BamHI (cdaA CD ) or NcoI/XhoI (glmM and glmM F369 ) and ligated with pET28b, which had been cut with the same enzyme. CdaA CD was cloned in frame with an N-terminal thrombin cleavable 6-histidine tag, while GlmM and GlmM F369 were cloned in frame with a C-terminal 6-histidine tag and a thrombin cleavage site was introduced in front of the His-tag as part of the primer sequence. The resulting plasmids pET28b-his-cdaA CD , pET28b-glmM-his, and pET28b-glmM F369 -his were initially recovered in E. coli XL1-Blue, yielding the strains ANG4583, ANG4584, and ANG4585 and subsequently transformed for protein expression into strain E. coli BL21(DE3), yielding strains ANG4597, ANG4598, and ANG4599, respectively. Plasmids pET28b-his-cdaA CD -R126, pET28b-glmM-D194A-his, pET28b-glmM-D151A/E154A-his were constructed for the expression of CdaA CD and GlmM alanine substitution variants. The plasmids were constructed by QuikChange mutagenesis using pET28b-his-cdaA CD and primer pair ANG3373/ANG3374 or plasmid pET28b-glmMhis and primer pairs ANG3381/ANG3382 and ANG3383/ 3384, respectively. The plasmids were initially recovered in E. coli XL1-Blue, yielding strains ANG5933, ANG5937, ANG5938 and subsequently introduced for protein expression into E. coli strain BL21(DE3) yielding strains ANG5940, ANG5944, ANG5945. In addition, plasmid pET28b-glmM-D151A/E154A/D194A-his for expression of a GlmM variant with a triple Asp151 (D151), Glu154 (E154), and Asp195 (D195) alanine substitution variant was constructed by Quik-Change mutagenesis using plasmid pET28b-glmM-D194A-his as template and primer pair ANG3383/3384 to introduce the D151A and E154A mutations. Plasmid pET28b-glmM-D151A/ E154A/D194A-his was recovered in E. coli strain XL1-Blue, yielding strain ANG5939 and subsequently introduced for protein expression into strain BL21(DE3) yielding strain ANG4946. The sequences of all plasmid inserts were verified by fluorescent automated sequencing at Eurofins.

Protein expression, purification, and quantification
Proteins CdaA CD , GlmM, and GlmM F369 were expressed and purified from 1 l cultures as previously described (28). Briefly, when bacterial cultures reached an OD 600 of approximately 0.6, protein expression was induced with 1 mM IPTG (final concentration) for 3 h at 37 C. Cells were harvested by centrifugation, suspended in 20 ml of 50 mM Tris pH 7.5, 500 mM NaCl buffered, and lysed using a French Press system. Lysates were clarified by centrifugation and the supernatant loaded onto a gravity flow column with 3 ml of Ni-NTA resin. Immobilized proteins were washed with 20 ml of 50 mM Tris pH 7.5, 500 mM NaCl, 50 mM imidazole buffer, and eluted in 5 × 1 ml fractions using 50 mM Tris pH 7.5, 200 mM NaCl, 500 mM imidazole buffer. Fractions containing the proteins were pooled and loaded onto a preparative Superdex 200 HiLoad 16/60 column equilibrated with one column volume of 30 mM Tris pH 7.5, 150 mM NaCl buffer. When appropriate, the purified proteins were concentrated using 10 ml 10 kDa cutoff Amicon concentrators for downstream applications. For the purification of the CdaA CD :GlmM and CdaA CD :GlmM F369 complexes or complexes of CdaA CD and GlmM alaninesubstitution variants, cell lysates of strains overproducing the respective proteins were mixed after the French press step, then the same protein purification procedure steps as described above used for the purification of individual proteins were performed. Protein concentrations were determined using the BCA assay kit (Pierce BCA Protein Assay Kit). For each sample, the readings were taken in triplicates and then averaged to obtain the protein concentration. Purified proteins were also separated on 12% SDS PAGE gels and detected by Coomassie staining.

Microscale thermophoresis
An MST experiment was performed to determine the binding affinity between the B. subtilis CdaA CD and GlmM proteins. The CdaA CD and GlmM were expressed and purified from 1 l cultures as described above, however, using 20 mM HEPES, pH 7.5, 500 mM NaCl buffer for the Ni-NTA purification and 10 mM HEPES, pH 7.5, 150 mM NaCl for the SEC purification step. Next, CdaA CD was fluorescently labeled with an amine-reactive dye using the Monolith Protein Labeling RED-NHS 2nd Generation kit (NanoTemper Technologies GmbH). To this end, 90 μl of a 40 μM CdaA CD solution was mixed with 10 μl of a 400 μM dye solution in 10 mM HEPES, pH 7.5, 150 mM NaCl, 0.05% Tween-20 buffer and incubated for 30 min at room temperature in the dark. Unincorporated dye was subsequently removed from the labeled protein as described in the manufacturer's instructions. Following the labeling reaction, the protein concentration was determined by nanodrop and using the Beer-Lambert equation and an extinction coefficient of 0.774 for CdaA CD . For the MST experiment, a 50 nM solution of the fluorescently labeled CdaA CD protein was mixed at a 1:1 ratio with a solution of purified GlmM protein at a starting concentration of 1600 μM and ten twofold dilutions there of prepared in the purification buffer (10 mM HEPES, pH 7.5, 150 mM NaCl, 0.05% Tween-20). The samples were filled into individual premium capillaries and subsequently loaded in the capillary tray. Each MST run was performed on a Monolith NT.115 instrument at a light emitting diode (LED) power of 95% and microscale thermophoresis (MST) power of 80% with a duration of 30 s laser on time (NanoTemper Technologies GmbH) (43). The experiment was performed five times and average normalized fluorescence values and standard deviations determined and plotted. For the data analysis and K d determination, the NT Analysis Software (NanoTemper Technologies GmbH) was used (43).

Protein crystallization, data processing, and analysis
For crystallization, the histidine tag was removed from the purified B. subtilis CdaA CD protein. This was done by incubating 10 mg purified protein with 20 U thrombin overnight at 4 C with agitation. The following day, the tag less CdaA CD was purified by size-exclusion chromatography as described above. The CdaA CD protein was crystallized at a concentration of 4 mg/ml in 0.1 M sodium cacodylate pH 6.5, 0.1 M ammonium sulfate, 0.3 M sodium formate, 6% PEG 8000, 3% γ-PGA via the vapor diffusion method. The crystal screens for B. subtilis GlmM (including the His tag) were set up at a concentration of 10 mg/ml and protein crystals were obtained in two different conditions. The structure with bound PO 4 (GlmM:PO 4 ) was obtained in the Morpheus screen containing 0.1 M buffer system 1 (Imidazole; MES, pH 6.5), 0.09 M NPS (NaNO 3 ; Na 2 HPO 4 ; (NH 4 ) 2 SO 4 ), and 37.5% MPD_P1K_P3350 (75% MPD, PEG 1K, PEG 3350) and the divalent-ion bound crystal structure (GlmM:metal ion) was obtained in 0.05 M Magnesium chloride hexahydrate, 0.1 M HEPES pH 7.5, 30% v/v Polyethylene glycol monomethyl ether 550 buffer. The crystals for the CdaA CD: GlmM F369 complex were set up at a protein concentration of 10 mg/ml and crystals were obtained in 0.12 M alcohols, 0.1 M buffer system (Imidazole; MES, pH 6.5) and 30% GOL_P4K (60% glycerol, PEG 4K) (Complex 1) and 0.1 M carboxylic acids, 0.1 M buffer system 1 (Imidazole; MES, pH 6.5) and 30% GOL_P4K (60% glycerol, PEG 4K) (Complex 2). The crystals were fished and stored in liquid nitrogen to test for diffraction at the I03 beamline at the Diamond Light Source (Harwell Campus). Data were reduced with DIALS (44) and scaled and merged with AIMLESS (45). The structures of CdaA CD and GlmM were solved by the molecular replacement method using the program MR-PHASER (46) in the Phenix suite (47), using the L. monocytogenes CdaA structure (PDB 4RV7; (21)) and B. anthracis GlmM structure (PDB 3PDK; (37)) as the search models, respectively. To solve the phase problem for the structure of the CdaA CD: GlmM F369 complex, dimers of B. subtilis CdaA CD and GlmM (each) were used as the search models using the MR-PHASER program in Phenix. The models were manually built using COOT (48) followed by iterative cycles of structure refinement using the Phenix-Refine program (49). The final refined structures were analyzed using the PDBePISA server (36) to identify buried interface areas for each protein. To search for conserved residues among the phylogenetically related homologs, a protein BLAST search was performed using B. subtilis CdaA CD and GlmM amino acid sequences as query sequences and a multiple sequence alignment (MSA) of the top 2500 homologs found in Firmicutes was prepared. The MSA was then used to identify conserved residues among the homologs using the ConSurf server (50).

CdaA CD activity and inhibition assays
To assess the activity of the B. subtilis CdaA CD enzymes, 20 μl enzyme reactions were set up in 100 mM NaCl, 40 mM HEPES pH 7 buffer containing 10 mM MnCl 2 (or 10 mM MgCl 2 or 10 mM CoCl 2 for metal dependent assays), 100 mM ATP spiked with a-P 32 -labeled ATP (PerkinElmer; using 0.4 μl of a 3.3 μM, 250 μCi solution per 20 μl reaction), and 5 μM CdaA CD enzyme. The mixture was incubated at 37 C for 4 h, followed by heat inactivation at 95 C for 5 min. After centrifugation for 10 min at 21,000g, 1 μl of the mixture was deposited onto a polyethylenimine-modified cellulose TLC plate (Millipore), and nucleotides separated by running the plate for 20 min using a 3.52 M (NH 4 ) 2 SO 4 and 1.5 M KH 2 PO 4 buffer system mixed at a 1:1.5 v/v ratio. Radioactive signals for ATP and the c-di-AMP reaction product were detected using a Typhoon FLA-700 phosphor imager. The bands were quantified using the ImageQuant program and the obtained values used to calculate the percent conversion of ATP to c-di-AMP. For the time course experiment, a 100 μl reaction mixture was prepared as described above and incubated at 37 C. Ten microliter aliquots were removed at the indicated time points and the enzyme reactions stopped by incubation the removed aliquots at 95 C for 5 min. To assess the activity of CdaA CD in the presence of GlmM or GlmM F369 , the full-length GlmM protein or C-terminally truncated GlmM variant was added to the reaction mixture at a 1:2 (CdaA CD : GlmM or CdaA CD : GlmM F369 ) molar ratio and the reactions incubated at 37 C for 4 h, stopped, and analyzed as described above. The enzyme activity assays were performed in triplicates with two independently purified protein preparations.

SAXS sample preparation and analysis
For the SAXS analysis, purified CdaA CD , GlmM, CdaA CD :GlmM complex, and CdaA CD :GlmM F369 complex protein samples were purified by size-exclusion chromatography as described above and subsequently concentrated to 5 mg/ml for CdaA CD , 24 mg/ml each for GlmM and the CdaA CD :GlmM complex and 10 mg/ml for the CdaA CD :GlmM F369 complex. Next, 50 μl protein samples were loaded on a high pressure Shodex column (KW403: range 10 kDa-700 kDa) fitted to an Agilent 1200 HPLC system at the B21 beamline at the Diamond Light Source. The size-exclusion column was equilibrated with 30 mM Tris pH 7.5, 150 mM NaCl buffer prior to loading the protein sample and the data were collected continuously throughout the protein elution. The analysis of the datasets was done via ScÅtter (51) using the scattering frames corresponding to the elution peaks. The ab initio analysis of the SAXS data to reconstruct a low-resolution shape of the model was done using the DAMAVER (DAM-MIF) program (52), which performs 13 ab initio runs to generate models from each run that were averaged to determine the most persistent three-dimensional shape of the protein. The cross-correlation Normalized Spatial Discrepancy (NSD) values were calculated using DAMAVER (DAMSEL) (52) from each of the 13 generated models. The mean NSD values calculated for each of the protein were: 0.591 ± 0.088 (CdaA CD ), 0.598 ± 0.014 (GlmM), 1.201 ± 0.099 (CdaA CD :GlmM F369 complex), and 0.661 ± 0.064 (CdaA CD :GlmM complex). The program Chimera (53) was used to visualize the reconstructed SAXS maps. The crystal structures of CdaA CD and GlmM dimers as well as CdaA CD :GlmM F369 complex were fitted in the respective SAXS envelopes in Chimera using the one-step fit function. For the CdaA CD : GlmM complex data, a structural model of the CdaA CD full-length GlmM complex was generated based on the crystal structure of the CdaA CD : GlmM F369 complex, which was then fitted into the SAXS envelope data using Chimera.