Activation mechanism of a small prototypic Rec-GGDEF diguanylate cyclase

Diguanylate cyclases synthesising the bacterial second messenger c-di-GMP are found to be regulated by a variety of sensory input domains that control the activity of their catalytical GGDEF domain, but how activation proceeds mechanistically is, apart from a few examples, still largely unknown. As part of two-component systems, they are activated by cognate histidine kinases that phosphorylate their Rec input domains. DgcR from Leptospira biflexa is a constitutively dimeric prototype of this class of diguanylate cyclases. Full-length crystal structures reveal that BeF3- pseudo-phosphorylation induces a relative rotation of two rigid halves in the Rec domain. This is coupled to a reorganisation of the dimeric structure with concomitant switching of the coiled-coil linker to an alternative heptad register. Finally, the activated register allows the two substrate-loaded GGDEF domains, which are linked to the end of the coiled-coil via a localised hinge, to move into a catalytically competent dimeric arrangement. Bioinformatic analyses suggest that the binary register switch mechanism is utilised by many diguanylate cyclases with N-terminal coiled-coil linkers.

The structure of native DgcR_AxxA (called DgcR_nat) was solved by molecular replacement to 2.2 Å 81 resolution. There is one dimer in the asymmetric unit with the protomers held together by extensive 82 isologous contacts between the Rec domains involving their α4 -β5 -α5 face (Fig. 1b). The Rec 83 domain shows the canonical (βα)5 fold (rmsd of 1.5 Å for 116 Cα atoms with respect to PhoP, 2PKX), 84 but with the C-terminal α5 helix considerably extended and forming together with its symmetry mate 85 a coiled-coil leading to the GGDEF domains. A Mg2+ ion is bound to the acidic pocket formed by 86 E12, D13, and the phosphorylatable D56. 87 The structure of the GGDEF domain is very similar to others in the PDB database (rmsd of 1.4 Å for 88 157 Cα atoms with respect to PleD, 2V0N) and shows the canonical (β1-α1-α2-β2-β3-α3-β4-α4-β5) 89 topology of nucleotidyl cyclases of group III (Sinha and Sprang, 2006) with an N-terminal extension 90 that starts with a characteristic wide turn showing a DxLT motif followed by helix α0 that leads to β1 91 ( Fig. 1b, see also (Schirmer, 2016). The GG(D/E)EF motif is located at the turn of the β2-β3 hairpin. 92 Again as observed in other structures (Wassmann et al., 2007), the guanine base of the substrate 93 analogue is bound to a pocket between α1 and α2 and forms H-bonds with N182 and D191, whereas 94 the two terminal phosphates are H-bonded to main chain amides of the short loop between β1 and α1. 95 Additionally, the γ-phosphate forms ionic interactions with K289 and R293. Two magnesium ions are 96 bound to the usual positions being complexed to the β-and γ-phosphates and the side-chain 97 carboxylates of D174, E217, and E218. 98 The GGDEF domains do not obey the 2-fold symmetry of the Rec domains, but form a relative angle 99 of about 90º. Thus, the two active sites with the bound GTP analogues do not face each other 100 rendering this constellation clearly non-productive. Though the constellation may be determined to 101 some extent by crystal packing, it demonstrates considerable inter-domain flexibility. Comparison of 102 the main-chain torsion angles reveals that the relative rotation can be traced back to a 169º change in a 103 single torsion, namely around the Cα -C bond of residue 136 (ψ136, Fig 2a). Thus, the hinge locates 104 to the C-terminal end of Rec α5, with the following residue I137 being packed against the Y149 from 105 the end of the GGDEF α0' helix in both chains (Figs. 2b and c). As noted before (Schirmer, 2016), the 106 conserved residue N146 (see sequence logo in Fig. 2 -figure supplement 1) is capping both α5 and 107 α0', but only in the A-chain. 108 The structure of activated DgcR_AxxA (called DgcR_act) obtained by BeF3-modification was solved 109 by molecular replacement to 2.8 Å resolution (Fig. 1c). There are two dimers in the asymmetric unit 110 that show virtually the same Rec dimer structure, but slightly different α5-helix bending and GGDEF 111 orientations (Figure 1-figure supplement 1). As in DgcR_nat, the dimer is formed by isologous 112 contacts between the α4-β5-α5 Rec faces and the extension of α5 forms a coiled-coil, but with an 113 altered relative disposition, which will be described in detail further below. D56 is found fully 114 modified by BeF3-and its immediate environment is different compared to DgcR_nat as will be 115 discussed in detail hereafter. The GGDEF domains are arranged symmetrical with the two bound 116 3'dGTP ligands facing each other, but too distant for catalysis (Fig. 1c, bottom). The GGDEF 117 orientation relative to the Rec domain is similar as in the A-chain of DgcR_nat. 118 Consistent with the crystal structures and the presence of the coiled-coil in both states, in solution, 119 DgcR is a constitutive dimer as measured by MALS both in the native and the activated form ( Figure  120 1-figure supplement 2). Addition of substrate analogue or product was not changing this quaternary 121 state. 122

Aspartate modification induces a relative rigid-body rotation within the Rec domain 123
Comparison of DgcR_act with DgcR_nat (Fig. 3a) shows that, on activation, the hydroxyl group of 124 T85 is moved towards the BeF3-moiety to form an H-bond. The void left by this movement is claimed 125 by Y105 that undergoes a small side-chain rotation, but does not change its rotamer. Furthermore, 126 K108 forms ionic interactions with BeF3-and E12 in the activated structure (Fig. 3a). In the native 127 state, a magnesium ion is bound loosely to E13 and D56, whereas, in the active state, it is additionally 128 coordinated by the BeF3-moiety. 129 Activation of DgcR is accompanied with a change in the backbone structure as identified by a 130 DynDom analysis (Girdlestone and Hayward, 2015). The Rec domain can be divided into two parts 131 that undergo a relative 16º rotation as shown in Fig. 3b. Thereby secondary structure elements α3 to 132 β5 (residues 54 to 108) behave as one rigid body (rmsd = 0.83 Å /49) that rotates relative to the rest 133 (8-53, 109-135) that superimposes with an rmsd of 1.19 Å for 67 Cα positions. Figure 3b shows that 134 the rotation axis passes roughly perpendicular to the β-sheet through the centre of β4 (L83). Note that 135 the phosphorylatable D56 is close to the junction between the two rigid bodies and that its Cα position 136 only changes slightly during the transition. T86, however, with its distance of 7.5 Å from the rotation 137 axis moves by 2.0 (Cα) to 3.3 Å (Oγ) and the motion is most pronounced (5.2 Å) for the N-terminus 138 of α3 (P91) with its distance of about 15 Å from rotation axis. Thus, the rigid body motion changes 139 significantly the arrangement of α4 with respect to α5, which has a profound effect on the packing of 140 the Rec domains in the dimer. 141 For many Rec domains, a Y-T coupling mechanism has been described, where, upon (pseudo-) 142 phosphorylation a threonine/serine (T86 in DgcR) is dragged towards the phosphate and the 143 conserved tyrosine/phenylalanine (Y105 in DgcR) follows suite with a rotameric change from 144 gauche+ to trans (Birck et al., 1999), (Bachhawat et al., 2005), (Wassmann et al., 2007). In DgcR, the 145 conserved tyrosine is already in trans conformation before activation and the T and Y move 146 concertedly towards the beryllofluoride moiety as part of a rigid-body (α3 to β5) movement (Fig. 3). 147

Rigid body rotation induces repacking of Rec domains within the dimer 148
In both states, the Rec domains form 2-fold symmetric dimers with the contacts mediated by 149 isologous interactions between the α4 -β5 -α5 surfaces (Fig. 4). However, due to the rigid-body 150 motion within the protomer and the concomitant relative displacement of α4 and α5 (Fig. 3), the 151 association of the α4 -β5 -α5 faces is different in the native and the activated state. Therefore, the 152 two dimers superimpose rather poorly (rmsd = 3.1 Å/119 Cα positions) with the β-sheets of the 153 protomers showing a difference in orientation of about 15º (Fig. 4a). 154 The native Rec dimer (Fig. 4b) with a buried surface area of 980 Å2 is held together by an extended 155 apolar contact of α5 (A117, F120) with α4 (F94, I98), an ionic interaction of D104 with R118, an H-156 bond between main-chain carbonyl 102 and R124 (both β5 -α5 contacts). All aforementioned 157 residues are well defined with the exception of the R118 side-chain, which probably has several 158 alternative conformations, but all placing the guanidinium group close to D104 and to its symmetry 159 mate. Finally, and most relevant for the allosteric regulation of the C-terminal GGDEF effector 160 domains, there are regular coiled-coil interactions across the symmetry axis between the C-terminal 161 halves of the α5 helices starting with S121. These will be discussed in the next chapter. 162 The activated Rec dimer (Fig. 4c) with a buried surface area of 850 Å2 shows the same apolar α5 -α4 163 cluster as the native dimer, but with the residues repacked in-line with the aforementioned relative 164 displacement of α4 and α5 within the protomer. At the centre of the interface, D104 shows a well-165 defined, intermolecular salt-bridge with R118, but also with R118 from the same chain. As in the 166 native dimer, the R124 and S121 side-chains form intermolecular H-bonds, but with other partners 167 compared to the native interactions (main-chain carbonyls of 98 and 103, respectively). 168 A BLAST search revealed that, apart from Rec -GGDEF orthologs, the sequence of the DgcR Rec 169 domain is most similar to that of OmpR-like transcription factors (Fig. 4d) (Bachhawat et al., 2005). Most of the 174 intermolecular interactions are thereby conserved, in particular the central salt-bridge D109 -R118 175 (DgcR numbering), or conservatively replaced (Fig. 4d). To our knowledge, no response regulator 176 with a DNA binding effector domain has yet been observed as a constitutive α4 -β5 -α5 dimer (for a 177 review, see (Gao et al., 2019), which is probably due to their small or absent coiled-coil linkers. 178 Summarizing, beryllofluoride-modification of D56 induces a relative rigid body motion in the Rec 179 domain that changes the relative disposition of α4 and α5. Consequently, since both helices are part of 180 the Rec -Rec interface, the relative arrangement of the protomers and, thus, of the two α5 helices of 181 the dimer is changed (compare top panels of Figs. 4b and c). This change is supposed to be crucial for 182 the allosteric regulation of the C-terminal GGDEF domains as will be discussed in the following. 183

Relative translation of C-terminal Rec helices changes coiled-coil register 184
The DgcR Rec α5 helix is longer by about 3 turns (10 residues) compared to that of canonical Rec 185 domains. In the dimer, these protrusions form a 2-fold symmetric coiled-coil both in the native and 186 the activated state (Figs. 1b-c), though with distinct relative arrangement. Both constellations are 187 stabilized by isologous contacts between predominantly hydrophobic residues that obey a heptad-188 repeat pattern (Figs. 5a and b). Thereby, I125 and L132 contribute to the contact in both structures 189 (position a; persistent contacts), but with the side-chains interacting with their symmetry mates from 190 opposite sides depending on the state (see e.g. the 132 -132 contact in Fig. 5a). In contrast, other 191 residues contribute either only to the native (L128, T135) or the activated (H129, A136) constellation 192 (positions d, e; conditional contacts). 193 The two contact modes represent alternative knobs-into-holes packing as best seen in the helical net Summarizing, the change in coiled-coil registration upon DgcR activation is accompanied by a 220 substantial shift between the constituting helices that lead directly to the catalytic domains. Structural 221 data on other DGCs are consistent with this finding. 222

Small rotation around inter-domain hinge allows formation of competent GGDEF dimer 223
In the activated structure, the two GGDEF domains show no mutual interactions and their precise 224 orientation appears to be determined by crystal contacts. However, the two bound 3'dGTP ligands 225 face each other, though their distance (> 10 Å) is clearly too large for catalysis (see Fig. 1c). Having 226 identified the CA -C main-chain bond of A136 as an inter-domain hinge (Fig. 2a) Most likely, deprotonation of the hydroxyl-group proceeds via a water molecule that could be 243 activated by the close-by metal(s) as e.g. in adenylate cyclases (Steegborn, 2014). 244 In the competent dimer, there are no clashes between the catalytic domains. Molecular dynamics 245 simulations would be required to refine the model, but it appears that D183 and D282 may interact 246 with Y286 and H187, respectively. All these residues are conserved in diguanylate cyclases ( ends of the coiled-coil is relieved by slight outward bending of the helices (Fig. 7d). Obviously, these 271 first three steps, which describe the transition of the native to the activated Rec stalk, will be tightly 272 coupled. 273 The following steps invoke no direct Rec -GGDEF communication, but only an unrestricted rotation 274 of the GGDEF domains around the inter-domain hinges. With the Rec stalk in its activated 275 constellation, the hinges are positioned such that the GGDEF domains can attain (4) a constellation as 276 in DgcR_act (Fig.7e) and, finally, assemble to form (5) the catalytically competent constellation 277 Michaelis-Menten complex (Fig.7f). An animation of the entire structural transition from native to 278 competent DgcR is shown in Fig.7g. 279 The aspect of conformational sampling and its dependence on the coiled-coil register and the 280 dynamics of the entire enzyme has been discussed before for PadC (Gourinchas et al., 2018). Whether 281 the asymmetric GGDEF dimer obtained for mutated PadC is of functional importance needs further 282 studies. Although such a state would probably be compatible with our model, it is not mandatory for 283 the proposed mechanism in which the two phosphodiester bonds could be formed quasi-284 simultaneously. Furthermore, we suggest that the competent GGDEF dimer would assemble 285 autonomously due to electrostatic and steric complementarity, in particular in presence of the 286 substrates that interact with K179 and M2 of the opposing domain ( Fig. 6c), thus not requiring any 287 direct interaction between input and output domains. 288

Allosteric inhibition by product mediated domain cross-linking 289
Allosteric product inhibition by c-di-GMP is a well-known feature of many DGCs (Christen et al. A very different behaviour was observed for activated DgcR (wt*) that produced very quickly (< 75 s) 315 a substantial amount of product yielding a lower boundary for kcat of 0.1 s-1 (Fig. 9a). This was 316 followed by a phase of very small, virtually constant velocity. Such phenotype was clearly 317 inconsistent with classical equilibrium models and seemed indicative of a slow transition to the 318 product-inhibited state. Mechanistically, this transition would comprise (fast) product binding and 319 (slow) re-organization of the two GGDEF domains to acquire the inactive product cross-linked 320 configuration (Fig. 8). 321 The progress curves were fitted with the kinetic model shown in Fig. 9b. Independent binding of two 322 substrate molecules (S) to the dimeric enzyme (EE) was parametrised with an equilibrium constant Kd 323 (assuming fast substrate binding), whereas the transition between active and inactive states was 324 modelled kinetically with an effective second-order rate constant kon (dependent on product and 325 enzyme concentration) and a first-order rate constant koff with the inhibitory constant given by Ki = 326 koff/kon. Note that for simplicity the model considers only one product binding site on the dimeric 327 enzyme, while there are actually four (two c-di-GMP dimers). This simplification will affect the 328 nominal value of Ki. Full kinetic modelling without this simplification and with explicit modelling of 329 the conformational enzyme transition has been postponed to a follow-up study. 330 The kinetic model fits the biphasic curve of wt* very well (Fig. 9a) yielding the parameters given in 331 Table 2. The kcat of 0.2 s-1 together with the slow kinetics of the active to inactive transition explains 332 the large build-up of product in the initial phase, which is followed by very low residual activity of the 333 (equilibrated) sample due to the low Ki of 62 nM. 334 To validate the involvement of the RxxD motif in feed-back product inhibition as suggested by the 335 crystal structure (Fig. 8) and shown for many other DGCs, but also to scrutinise the kinetic model, the 336 motif was mutagenised to AxxA. Indeed, the activated mutant (mutAxxA*) was found to be drastically, 337 though not fully, inhibition relieved (Fig. 9a, inset). The curve is consistent with an unchanged kcat, 338 but a drastically (almost 200-fold) increased Ki as compared to wild-type (Tab. 2). Apparently, the 339 mutations did not completely abolish inhibition with the remaining residues of the primary and 340 secondary I-site possibly still enabling (weak) product binding (Fig. 8). 341 In contrast to the native wild-type enzyme (wt), the activity of the native mutant (mutAxxA) was lower, 342 which may be due to a detrimental, long-range effect of the mutations on the active site geometry. 343 Notably, there was no indication of product inhibition. Thus, for both wild-type and mutant DgcR the 344 activated state is more susceptible to product inhibition. Whether this is due a sub-optimal product 345 mediated backside cross-linking in the native state as suggested by the crystal structure (Fig. 8) has to 346 await further structural investigations. 347 Summarizing, activated DgcR shows a pronounced initial burst of activity before entering the product 348 inhibited state with a rather slow kinetics probably reflecting domain reorganization. The kinetic 349 model (Fig. 9b) proved to reproduce all measured progress curves and the parameters (Tab. 2) reflect 350 the impact of activation and Ip-site mutation. 351

Rec -GGDEF linker sequence profiles are consistent with register shift mechanism 352
DgcR has been selected as a prototypic Rec -GGDEF enzyme of relatively small size (298 residues), 353 but bioinformatic analysis showed that the linker length can vary considerably in this class of DGCs. 354 This was surprising considering that the linker has a defined structure and seems crucial for signal 355 transduction. However, the linker length histogram (Fig. 10a) shows that the lengths are not 356 distributed uniformly, but exhibit discrete values separated by multiples of 7 (groups 1 to 6, with 357 DgcR and WspR belonging to groups 1 and 4, respectively). Thus, members of the groups would 358 merely differ in the number of double helical turns when forming parallel coiled-coils. Indeed, the 359 individual sequence logos can easily be aligned (Fig. 10b) to reveal the striking repeat of leucines 360 in every 7th position (heptad position a). Most interestingly, the last (and to a lesser degree the last but 361 one) heptad repeat at the C-terminal end (Fig. 10c) shows a conserved axxdexx pattern as in DgcrR 362 (Fig. 5). Thus, a common binary register shift mechanism seems likely for members of all the 363 groups. Group 0 (Figs. 10a, b) does not obey the linker length rule. Since it also has an (S/N)PLT 364 instead of a DxLT motif, it probably has a different linkage and, therefore, activation mechanism. respective DGCs has not been studied, but it will surely affect the relative disposition of the hinges 395 that lead to the catalytic domains and, thus, activity. 396 Apparently, the coiled-coil linker is a versatile and effective means of transmitting a signal between 397 domains without requiring direct interactions between them, which, obviously, is of paramount 398 advantage for their modular combination in evolution. The same principle seems to apply also for 399 HKs, many of them both are controlled by the same kind of input domains as DGCs and exhibit a 400

BeF3-modification of DgcR 420
In order to produce BeF3-modified DgcR, approximately 300 μM of DgcR in 20 mM Tris pH 8.0, 20 421 mM NaCl and 5 mM MgCl2 were incubated with a mixture of NaF at 10 mM and BeCl2 at 1 mM, 422 final concentration. After gentle mixing to achieve a homogeneous solution, the sample was left at 423 room temperature for at least 15 minutes. DgcR BeF3-mix was then centrifuged at 4ºC at 18.000 x g 424 to remove a light precipitation formed during the process. Protein concentration was measured after 425 the activation process and was found virtually unaltered. 426

SEC-MALS analysis 427
Light scattering intensity and protein concentration were measured at elution from the column using 428 an in-line multi-angle light-scattering and differential refractive index detectors (Wyatt Heleos 8+ and 429 Optilab rEX). These data were used to calculate molar mass for proteins by standard methods in Astra to the c-di-GMP product were integrated and converted to concentrations using a scale factor obtained 471 from calibration. Data was plotted and fitted using proFit (QuantumSoft). 472 To calculate theoretical progress curves, the partial differential equations corresponding to the kinetic 473 scheme in Fig. 9b were set-up in ProFit and solved by numerical integration. Global fitting of this 474 function using the Levenberg algorithm implemented in ProFit to the measured time courses of 475 product and substrate concentration yielded the parameters listed in Table 2.         has been derived from the DgcR homologs of group 1 (see Fig. 10). Important residues are indicated by their number in DgcR (in bold for residues involved in c-di-GMP feed-back inhibition, see Fig. 8). Arrows indicate putative residues engaged in inter-domain contacts in the competent GGDEF dimer arrangement (Fig. 6b). R147 may interact with the Hogsteen-edge of the guanyl-base of the substrate bound to the opposing domain.       The structures are represented as in Figs. 1b,c, but with the residues of the conditional coiled-coil contacts shown as CPK models (residues in d and e position are shown is pink and green). The beryllofluoride moieties of the dimer are highlighted by magenta circles. a) DgcR_nat, symmetrized version with both GGDEF domains in B-chain orientation (cf. with Fig. 1b).
b) As in a, but with beryllofluoride-induced tertiary change applied to Rec rigid_body 1 (see Fig. 3).
c) As in b, but with quaternary change applied to Rec domains. Note the clash between the C-terminal ends of the coiled-coil (red circle). d) As in c, but with Rec dimer as found in symmetrized version of DgcR_act. e) Symmetrized version of DgcR_act (cf. with Fig. 1c).
f) Model of catalytically competent DgcR as in Fig. 6b. g) Animation (two views) of the structural transitions between the states shown in panels a to f obtained by morphing. The magenta broken lines (top view, right) connect the reacting atoms of the two substrates, i.e. O3' with Pα of the opposing substrate.  Table 2. b) Kinetic model of diguanylate cyclase activity controlled by non-competitive product binding. Substrate (S) binding to the dimeric enzyme (EE) is modeled with the equilibrium dissociation constant Kd and assumed to be unaffected by the presence of S in the second binding site or of product (P) in the allosteric site. Product binding is modeled kinetically with rate constants kon and koff. Note that the model considers simply one instead of four product binding sites on the enzyme. Only the Michaelis-Menten complex with two bound substrate molecules and no bound product (SEES) is competent to catalyze the S + S → P condensation reaction (with turn-over number kcat).