The allosteric activation of cGAS underpins its dynamic signaling landscape

Cyclic G/AMP synthase (cGAS) initiates type-1 interferon responses against cytosolic double-stranded (ds)DNA, which range from antiviral gene expression to apoptosis. The mechanism by which cGAS shapes this diverse signaling landscape remains poorly defined. We find that substrate-binding and dsDNA length-dependent binding are coupled to the intrinsic dimerization equilibrium of cGAS, with its N-terminal domain potentiating dimerization. Notably, increasing the dimeric fraction by raising cGAS and substrate concentrations diminishes duplex length-dependent activation, but does not negate the requirement for dsDNA. These results demonstrate that reaction context dictates the duplex length dependence, reconciling competing claims on the role of dsDNA length in cGAS activation. Overall, our study reveals how ligand-mediated allostery positions cGAS in standby, ready to tune its signaling pathway in a switch-like fashion.

Resting cGAS is thought to be an inactive monomer, and formation of a 2:2 dimer with dsDNA within the catalytic domain (human cGAS residue 157 -522) is necessary for activation (2 cGAS molecules on two dsDNA strands [Li et al., 2013;Zhang et al., 2014]). cGAS recognizes dsDNA independent of sequence (Gao et al., 2013b;Kranzusch et al., 2013;Li et al., 2013;Zhang et al., 2014), thus it was initially proposed that any dsDNA long enough to support the dimerization of cGAS could activate the enzyme equally well (e.g.~15 base-pairs, bps (Chen et al., 2016a;Li et al., 2013;Zhang et al., 2014)). However, it was long known that dsDNA of at least 45 bp was required to elicit IFN-1 responses in cells (Chen et al., 2016a;Stetson and Medzhitov, 2006;Unterholzner et al., 2010). Indeed, two recent studies demonstrated that cGAS discriminates against short dsDNA (Andreeva et al., 2017;Luecke et al., 2017). For instance, cGAS is minimally activated in cells by dsDNA shorter than 50 bps, and maximal activation requires dsDNA longer than 200 bps, with the length-dependence more pronounced at lower dsDNA concentrations (Andreeva et al., 2017;Luecke et al., 2017). The dependence on dsDNA length is thought to arise because cGAS dimers linearly propagate along the length of two parallel dsDNA strands without making inter-dimer contacts, consequently generating a ladder-like complex that increases the overall stability via avidity (Andreeva et al., 2017). Together, it is believed that dsDNA length-based signal-to-noise filtration occurs at the binding/recognition stage (i.e. different K D s for different dsDNA lengths), but not at the signal transduction step (i.e. same V max for different dsDNA lengths (Andreeva et al., 2017)). eLife digest The human immune system protects the body from various threats such as damaged cells or invading microbes. Many of these threats can move molecules of DNA, which are usually only found within a central compartment in the cell known as the nucleus, to the surrounding area, the cytoplasm.
An enzyme called cGAS searches for DNA in the cytoplasm of human cells. When DNA binds to cGAS it activates the enzyme to convert certain molecules (referred to as 'substrates') into another molecule (the 'signal') that triggers various immune responses to protect the body against the threat. To produce the signal, two cGAS enzymes need to work together as a single unit called a dimer.
The length of DNA molecules in the cytoplasm of cells can vary widely. It was initially thought that DNA molecules of any length binding to cGAS could activate the enzyme to a similar degree, but later studies demonstrated that this is not the case. However, it remains unclear how the length of the DNA could affect the activity of the enzyme, or why some of the earlier studies reported different findings.
Hooy and Sohn used biochemical approaches to study the human cGAS enzyme. The experiments show that cGAS can form dimers even when no DNA is present. However, when DNA bound to cGAS, the enzyme was more likely to form dimers. Longer DNA molecules were better at promoting cGAS dimers to form than shorter DNA molecules. The binding of substrates to cGAS also made it more likely that the enzyme would form dimers. These findings suggest that inside cells cGAS is primed to trigger a switch-like response when it detects DNA in the cytoplasm.
The work of Hooy and Sohn establishes a simple set of rules to predict how cGAS might respond in a given situation. Such information may aid in designing and tailoring efforts to regulate immune responses in human patients, and may provide insight into why the body responds to biological threats in different ways.
Our understanding of the mechanisms by which cGAS is activated has evolved over the years, yet it remains unclear why two conflicting views on the role of dsDNA length have existed. Moreover, we noted that neither the previous (dsDNA length-independent) nor current (dsDNA length-dependent) activation model provides a robust framework for understanding how cGAS might be able to shape its diverse signaling landscape. First, the relationship between dsDNA binding and activation is poorly established. For instance, it remains to be tested whether the initial dsDNA binding step alone sufficiently explains the dsDNA length-dependent activation of cGAS in cells. Second, the ladder model implies that dimerization efficiency continuously increases with dsDNA lengths (>1000 bps), while the optimal cellular response peaks with any dsDNA longer than~200 bps (Andreeva et al., 2017). Third, the ladder model is heavily based on structural and functional studies of the catalytic domain of cGAS (cGAS cat ). It was recently proposed that the N-domain of cGAS binds dsDNA and plays a crucial role in its cellular function (Tao et al., 2017;Wang et al., 2017). Moreover, dsDNA binding by the N-domain is thought to enhance the activity of the monomeric enzyme, consequently lifting the dsDNA length restriction (Lee et al., 2017). Thus, it is not clear whether the ladder-like arrangement applies exclusively to cGAS cat , or whether it is germane to the full-length protein (cGAS FL ). Finally, given that cGAS is the predominant sensor for cytoplasmic dsDNA (Chen et al., 2016a), it is imperative for this enzyme to amplify and attenuate its signaling cascade in a switch-like manner to ensure proper host responses. How cGAS achieves this important task remains poorly understood.
We find here that human cGAS can auto-dimerize without dsDNA. dsDNA regulates this intrinsic monomer-dimer equilibrium not only in a cooperative, but also in a length-dependent manner. Also unexpectedly, substrates (ATP/GTP) can pull cGAS into the dimeric state without dsDNA. Because ligand binding is coupled to dimerization, the length of dsDNA not only regulates binding and dimerization (signal recognition), but also the substrate binding and catalysis (signal transduction). Compared to cGAS cat , cGAS FL auto-dimerizes more readily and also couples binding of both substrate and dsDNA to dimerization more efficiently, revealing a new function of the N-domain in potentiating the dimerization of cGAS. Dimerization is essential for dsDNA-mediated activation of both cGAS FL and cGAS cat , and the dimers do not arrange in an ordered configuration on long dsDNA, suggesting the role of dsDNA length is to simply regulate the probability of dimerization. Importantly, shifting the monomer-dimer equilibrium via elevated enzyme and ATP/GTP concentrations in the absence of dsDNA does not override the requirement for dsDNA to activate cGAS. Instead, these other factors prime the enzyme to be activated even by short dsDNA, indicating that the dependence on duplex length can change according to cellular reaction context. Together, our results set forth a unifying activation model for cGAS in which the intrinsic monomer-dimer equilibrium poises the enzyme to dynamically turn on or off its signaling pathway in a switch-like fashion.

Results
Human cGAS cat can dimerize without dsDNA Human cGAS cat (denoted as cGAS cat hereafter) eluted as two peaks in size-exclusion chromatography (SEC) depending on protein concentration ( Figure 1A). With decreasing protein concentrations, the two peaks progressively merged into the one with the lower apparent molecular weight ( Figure 1A), suggesting that cGAS cat is subject to an intrinsic monomer-dimer equilibrium without dsDNA ( Figure 1-figure supplement 1). This was surprising, as previous studies showed that mouse cGAS cat behaved as a monomer (Li et al., 2013); we speculate that mouse-cGAS cat intrinsically dimerizes more weakly.
To further test the intrinsic dimerization capability of cGAS, we examined the oligomeric state using small-angle-x-ray-scattering (SAXS; Figure 1B). The radius of gyration (R g ) and the maximum diameter (D max ) for apo-cGAS cat at all tested concentrations aligned better with those of dsDNAbound mouse-cGAS cat dimer ( Figure 1C-D; [Li et al., 2013]). We analyzed the distrbution of monomeric and dimeric species using SAXS-estimated molecular weight (SAXS MoW2) and OLIGOMER in ATSAS ( Figure 1D [ Mylonas and Svergun, 2007;Petoukhov et al., 2012;Petoukhov and Svergun, 2013]). Here, the fraction of dimeric species was proportional to protein concentrations, and the dimerization constant was estimated to be~20 mM ( Figure 1D). Together, we concluded that cGAS has an intrinsic capacity to dimerize, albeit with low affinity.

cGAS behaves like a classic allosteric enzyme
In allosteric signaling enzymes, incoming signal (activator) and substrates either exclusively or preferentially bind to the active state and stabilize the corresponding conformation (Koshland et al., 1966;Monod et al., 1965;Sohn et al., 2007;Sohn and Sauer, 2009). Such a coupling mechanism synchronizes conformational states with activity states, thereby allowing the enzymes to generate switch-like responses (Koshland et al., 1966;Monod et al., 1965;Sohn et al., 2007;Sohn and Sauer, 2009). Importantly, preferential, but not exclusive ligand binding to the active state grades signaling output, as the distribution of active and inactive species is dictated by the relative binding affinity of different activators to either state (Monod et al., 1965;Sohn and Sauer, 2009;Tsai and Nussinov, 2014). Our observation that cGAS can dimerize on its own suggests a new framework for understanding its activation mechanism ( Figure 2A). Here, apo-cGAS is placed in an intrinsic allosteric equilibrium where it is predominantly an inactive monomer under normal conditions. Overexpression (Ma et al., 2015), substrate binding, and cytoplasmic dsDNA synergistically activate cGAS by promoting dimerization. Furthermore, given that monomeric cGAS binds dsDNA (Andreeva et al., 2017;Li et al., 2013), it is possible that dsDNA length determines the fraction of active dimers ( Figure 2B), thus underpinning the duplex length dependent cellular activity (Andreeva et al., 2017;Luecke et al., 2017). Below, we describe a series of experiments to further test and develop this allosteric framework for understanding the activation of cGAS.
The cellular activity of cGAS is dsDNA length-dependent (Andreeva et al., 2017;Luecke et al., 2017), as if the enzyme uses duplex length as a ruler to differentiate between signal and noise. Currently, it is believed that this length-based noise filtration occurs only at the initial encounter step,   Here, cGAS is subject to an intrinsic allosteric equilibrium with two major activity/conformational states, namely inactive monomer and active dimer. Resting cGAS is predominantly an inactive monomer (top). dsDNA (length-dependent) binding, increasing cGAS concentration, and substrate binding synergistically drive the allosteric equilibrium toward the active dimer. (B) An allosteric model describing dsDNA length-dependent Figure 2 continued on next page with longer dsDNA invoking a ladder-like arrangement (Andreeva et al., 2017). However, all previous binding studies entailed raising cGAS concentrations (Andreeva et al., 2017;Li et al., 2013), which intrinsically alters the dimer population. Thus, we re-examined the coupled relationship between dsDNA-binding and dimerization without altering the intrinsic dimerization equilibrium. First, using both direct and competition methods, we observed that cGAS cat indeed binds dsDNA in a length-dependent manner ( [Andreeva et al., 2017;Du and Chen, 2018;Ma et al., 2015]).
Increasing concentrations of 24 bp dsDNA did not induce significant changes in FRET ratios ( Figure 2C), consistent with the previous report that such a short dsDNA binds cGAS but cannot induce dimerization (Andreeva et al., 2017). With longer dsDNA, we observed more robust changes in FRET signals ( Figure 2C). Importantly, the half-maximal dsDNA concentrations necessary to induce the FRET signal (K FRET ) decreased with longer dsDNA, with the optimum length reaching at~300 bps ( Figure 2C-D). The maximal change in FRET ratio also generally increased with longer dsDNA, suggesting the dimeric fraction increased with longer dsDNA ( Figure 2C). The fitted Hill constants in these experiments were between 1.5 and 2, indicating that dsDNA-induced dimerization is a cooperative process ( Figure 2E). Overall, our results confirm that dsDNA binding and dimerization are directly coupled, consistent with the idea that the intrinsic monomer-dimer equilibrium underpins the dsDNA length discrimination by cGAS (Figure 2A-B).
It is thought that cGAS does not bind ATP/GTP in the absence of dsDNA, as the loops surrounding the active site would block substrate entry (Gao et al., 2013b). However, cGAS can bind cGAMP in the absence of dsDNA, and multiple crystal structures indicate that the B-factors of loops surrounding the active site are 5 to 20-fold higher than the protein core, suggesting cGAS might be able to weakly interact with ATP/GTP even without dsDNA (e.g. PDB IDs: 4k8v, 4o69, and 4km5; (Gao et al., 2013b;Kranzusch et al., 2013;Zhang et al., 2014)). Thus, we tested whether ATP/GTP and their nonhydrolyzable analogues (AMPcPP/GMPcPP) induce dimerization via our FRET assay. Here, introducing substrates increased the FRET ratio, albeit to a lower extent than long dsDNA ( Figure 2F), suggesting that substrates alone can pull cGAS cat into the dimeric state to some degree. The lower capacity of AMPcPP/GMPcPP to induce FRET changes is consistent with our observations that the analogues bind more weakly than ATP/GTP (K i = 280 mM (Figure 2-figure supplement 1D) vs. K M of~100 for ATP/GTP with dsDNA, see Figure 3 below). Together, our results suggest that the fraction of active, dimeric cGAS would be partitioned according to the length of dsDNA and the availability of substrates ( Figure 2A). Thus, our results support that cGAS employs a strategy similar to classical allosteric enzymes to generate a graded output.

A new quantitative assay for cGAS enzymatic activity
All published methods that quantitatively monitor the enzymatic activity of cGAS track cGAMP, and are not ideal for mechanistic studies due to their low throughput or difficulty in saturating the enzyme with substrates (e.g. TLC, HPLC-Mass-Spec, and fluorescently-labeled ATP/GTP; (Andreeva et al., 2017;Gao et al., 2013b;Hall et al., 2017;Vincent et al., 2017)). cGAS generates two inorganic pyrophosphates (PP i ) per cGAMP. Thus, we adapted a pyrophosphatase (PP i ase)-  Figure 3A; (Seamon and Stivers, 2015)). Using this assay, we found that cGAS cat produces PP i most efficiently in the presence of a 1:1 mixture of ATP and GTP plus dsDNA ( Figure 3B;>90% of its NTase activity produces cGAMP when ATP and GTP are equimolar (Gao et al., 2013b)). Moreover, no PP i production was observed from an inactive cGAS variant (E225A-D227A-cGAS cat (Gao et al., 2013b); Figure 3B), and the activity of PP i ase was not rate-limiting (Figure 3-figure supplement 1). Thus, we concluded that the PP i ase-coupled assay provides a robust method to quantitatively monitor the enzymatic activity of cGAS.

dsDNA length regulates the extent of activation
Our experiments thus far support an activation model in which dsDNA length determines the distribution between active dimers and inactive monomers (Figure 2A-B). This mechanism entails different dsDNA lengths to produce graded maximal signaling output (V max ) even at saturating concentrations (Sohn and Sauer, 2009). In contrast, it has been proposed that the dsDNA lengthdependent activity of cGAS arises solely at the signal recognition step (binding), but not at the signal transduction step (enzymatic step; (Andreeva et al., 2017)). However, the authors could not conduct their studies under steady-state conditions due to the use of fluorescently-labeled substrates (Andreeva et al., 2017). Because our coupled-assay eliminates this issue, we directly tested whether dsDNA length could regulate the enzymatic activity of cGAS. Here, we found that cGAS cat has low basal activity without dsDNA (180 ± 30 M À1 min À1 ), which can be increased by 50-fold with >300 bp dsDNA ( Figure 3C). dsDNA concentrations required to induce the half-maximal activity of cGAS cat increased with shorter dsDNA (K act ; Figure 3C and  (Andreeva et al., 2017). Importantly, the maximum dsDNA-induced activity (k max ) also decreased with shorter dsDNA ( Figure 3C  , which is in contrast to the previous report proposing that the role of dsDNA length is limited to binding (Andreeva et al., 2017). Moreover, normalizing the k max by K act for each dsDNA length showed that the overall signaling efficiency of cGAS cat (dsDNA binding and maximum output) changes more drastically compared to either parameter alone ( Figure 3D, see also Figure 3-figure supplement 2A-C). For instance, the overall signaling efficiency changes by nearly 100-fold between 24 to 339 bp dsDNA, while either binding or maximal activity alone changes only up to 10-fold ( Figure 3D, see also Figure 3-figure supplement 2A-D). Together, our observations indicate that cGAS discriminates against short dsDNA not only at the initial recognition step, but again at the signal transduction step, resulting in two-stage dsDNA length discrimination.
dsDNA length regulates formation of the enzyme-substrate complex (K M ) and the turnover efficiency (k cat ) of cGAS We next determined substrate turnover kinetics in the presence of various dsDNA lengths. Without dsDNA, cGAS cat showed measurable NTase activities (Figure 3-figure supplement 1B). With saturating dsDNA longer than 300 bps, the K M of cGAS cat for ATP/GTP was near 100 mM, and the k cat was 5 min À1 ( Figure 3E and Figure 3-figure supplement 2D). The observed K M for ATP/GTP is comparable to previously reported values measured using Surface Plasmon Resonance (SPR) and rapid-fire Mass-Spec for both human and mouse enzymes (Hall et al., 2017;Vincent et al., 2017). Moreover, the relatively slow k cat is consistent with a report indicating that human cGAS is considerably slower than mouse cGAS (~20 min À1 ) . Considering intracellular concentrations of ATP and GTP are >1 mM and~500 mM, respectively (Chen et al., 2016b;Traut, 1994), our result suggests that once cGAS encounters cytoplasmic dsDNA, one cGAMP would be generated in less than 20 s, compared to about one per 15 min in the absence of dsDNA. With shorter dsDNA, the K M increased about 2-fold, and the k cat decreased up to 4-fold (Figure 3-figure supplement  2D). Combined, our results indicated that the overall catalytic efficiency of cGAS can change up to 8-fold (k cat /K M ) by the length of bound dsDNA ( Figure 3F and Figure 3-figure supplement 3D). On another note, the fitted Hill constants in these experiments were near two for all dsDNA lengths (Figure 3-figure supplement 2D), consistent with the observation from mouse cGAS cat . Because most cGAS cat populations would be dimeric with saturating long dsDNA, the observed cooperativity is likely from substrate-substrate interactions (i.e. ATP binding enhances GTP binding or vice versa; ). Overall, these results further support that dsDNA length can grade the enzymatic activity of cGAS.

The N-domain potentiates cGAS dimerization
It was recently reported that the N-domain of cGAS (residues 1 -156) plays an important role in vivo by providing an additional nonspecific dsDNA binding site (Tao et al., 2017;Wang et al., 2017). Moreover, it was proposed that the N-domain reduces the requirement for long dsDNA, because it facilitates the activation of monomeric mouse cGAS (Lee et al., 2017). To test whether our findings using cGAS cat still apply to the full-length enzyme, we generated recombinant cGAS FL . The fulllength protein eluted as two peaks in SEC ( Figure 4A and Figure), behaved as an extended particle by SAXS ( Figure 4B, and Figure 4-figure supplement 1B-C), and was free from nucleic acid contamination ( Figure 4-figure supplement 1A). Of note, it appeared that cGAS FL has a higher dimerization propensity compared to cGAS cat , as indicated by broader peak distribution at 15 mM ( Figure 4A vs. Figure 1A). Supporting this notion, SAXS analyses also suggested that the dimerization constant of cGAS FL is about 2-fold less than cGAS cat at~7.5 mM (Figure 4-figure supplement 1B-C; cGAS cat is 48% dimeric at 15 mM; Figure 1C-D). To further test that the N-domain can dimerize we generated recombinant N-domain (cGAS N ) and found that it migrated as a dimer in SEC, and also behaved as an extended dimer in SAXS (Figure 4-figure supplement 2A-C). Of note, in our solution equilibrium assay, cGAS N bound dsDNA much more weakly than cGAS cat , which is in contrast to the non-equilibrium mobility assay used by Tao  , further corroborating that the full-length enzyme couples substrate binding to dimerization more efficiently due to its enhanced intrinsic dimerization activity. We also found that dsDNA length still grades K act and k max of cGAS FL , as observed with cGAS cat ( Figure 4E, Figure 4figure supplement 3D); K M and k cat for cGAS FL were also graded according to dsDNA lengths ( Figure 4F, Figure 4-figure supplement 3E-F). Overall, our observations indicate that cGAS FL and cGAS cat operate within the same molecular framework, and reveal a new role for the N-domain in potentiating the dimerization of cGAS.

Dimerization is required for dsDNA-mediated activation
Although 24 bp dsDNA failed to induce dimerization ( Figures 2C and 4C), it activated cGAS to a significant extent (Figures 3C and 4E). Monomeric cGAS can also bind dsDNA, but it is thought to be poorly activated (Andreeva et al., 2017;Li et al., 2013). Moreover, it was proposed that the N-domain enhances the dsDNA binding of monomeric cGAS (Tao et al., 2017), thereby activating the enzyme by lifting the dimerization requirement (Lee et al., 2017). Nonetheless, 24 bp dsDNA bound and activated both cGAS cat and cGAS FL only moderately ( Figures 3C and 4E). Thus, our data are most consistent with the allosteric model in which the presence of ATP/GTP increased the dimeric fraction, allowing the short dsDNA to activate cGAS to some extent (Figure 2A-B). To We predict that the dsDNA length dependence of K394E-cGAS FL likely arise from the dimerization of the N-domain. Importantly, without dsDNA, K394E-cGAS showed similar activities as wild-type; however, dsDNA failed to stimulate the enzymatic activity of the mutants regardless of duplex length ( Figure 5C-F). For instance, dsDNA marginally decreased the K M of K394E-cGAS, but the k cat did not increase significantly ( Figure 5D and F). Our results also support the idea that monomeric cGAS can bind substrate and is basally active, yet dimerization is necessary for dsDNA-and dsDNA length-dependent activation regardless of the intact N-domain. Furthermore, our observations support the idea that short dsDNA and substrates can synergistically activate cGAS (see also Figure 7 below).
cGAS dimers appear to arrange randomly on dsDNA cGAS dimers are thought to form a ladder-like array along the length of dsDNA to maximize the stability of its signaling complex (Andreeva et al., 2017). Given that both cGAS monomers and dimers bind dsDNA (Andreeva et al., 2017;Li et al., 2013), our results are better explained by a simpler mechanism in which dsDNA length regulates the fraction of cGAS dimers without invoking an ordered structure (Figure 2A-B). To further test this idea, we imaged cGAS cat and cGAS FL with dsDNA using nsEM ( Figure 6; see also Figure 6-figure supplement 1 for zoom-in images, and additional images in Figure 6-figure supplement 2). When proteins were in excess over dsDNA, we observed large clusters likely reflecting multiple cGAS dimers binding to several different dsDNA strands ( Figure 6A and E). It is possible that these clusters reflect the recently observed phase-shifting condensates of cGAS . dsDNA (Du and Chen, 2018). With excess dsDNA over protein, which more likely resembles in vivo events when dsDNA breaches the cytoplasm, it appeared that cGAS dimers randomly decorated dsDNA ( Figure 6B and F), with the particle sizes corresponding to the dimeric species of cGAS cat and cGAS FL , respectively (i.e. the D max for these constructs are~10 and 18 nm, respectively; Figure 1). Importantly, the ladder-like arrangement of cGAS particles was rare for both cGAS cat and cGAS FL ( Figure 6B and F, Figure 6-figure supplement 2D-E), suggesting that cGAS.dsDNA does not form an ordered supra-structure.
On the other hand, the size of particles resulting from excess K394E-cGAS cat with dsDNA appeared smaller and corresponded to the D max of cGAS monomers ( Figure 6C; see also Figure 5figure supplement 1), likely reflecting monomeric cGAS randomly bound on dsDNA. For K394E-cGAS FL , we observed dsDNA-bound clusters somewhat similar to wild-type (these clusters are likely mediated by the intact N-domain that promotes dimerization). However, the clusters were not as expansive as those formed by wild-type ( Figure 6E vs. G). Moreover, we did not observe any significant decoration of dsDNA when the K394E mutants were present in sub-stoichiometric amounts  Figure 6D and H; the particle size observed in Figure 6H also corresponds to the monomeric fulllength cGAS). Overall our nsEM experiments support the allosteric framework of cGAS (Figure 2A -B) in which the role of dsDNA length is to simply bias the fraction of active dimers without necessitating supramolecular assemblies. Nevertheless, given the low-resolution imaging of nsEM, future structural studies are warranted to more fully understand the nature of these cGAS.DNA complexes. Ratios of protein to dsDNA or dsDNA to protein are binding site normalized; 18 bp per binding site. The particle sizes in B and F are consistent with the D max of cGAS cat and cGAS FL , respectively (Figures 1 and 4). The context-dependent, allosteric activation of cGAS It was initially proposed that dsDNA length does not play a significant role in regulating the activation of cGAS (Gao et al., 2013b;Kranzusch et al., 2013;Li et al., 2013); however, two recent studies have contested this model (Andreeva et al., 2017;Luecke et al., 2017). The reason for this discrepancy is still unclear. Our results suggest that raising enzyme and substrate concentrations increases the dimeric fraction of cGAS, while binding of short dsDNA cannot (e.g. 24 bp). Given the vastly different cGAS and substrate concentrations used in previous studies (Andreeva et al., 2017;Gao et al., 2013b;Kranzusch et al., 2013;Li et al., 2013;Luecke et al., 2017), we speculated that the apparent or lack of dsDNA length-dependence is caused by the fraction of cGAS dimers formed without dsDNA (Figure 2A). To test this idea, we monitored the steady-state NTase activity of cGAS cat and cGAS FL with saturating amounts of various dsDNA lengths and a permutation of high and low concentrations of enzyme and ATP/GTP ( Figure 7A-D). Increasing substrate and enzyme concentrations did not eliminate the need for dsDNA. However, the dependence on dsDNA length progressively decreased with increasing protein and substrate concentrations. For instance, with low cGAS cat and sub-K M ATP/GTP concentrations (cGAS is predominantly monomeric), we observed strong dsDNA length-dependent activities, with a difference of 8-fold between 24 bp and 564 bp dsDNA ( Figure 7A). With low cGAS and high ATP/GTP, the difference between short and long dsDNA was 4-fold ( Figure 7B). With high cGAS and low ATP/GTP, the difference was again reduced to 2.5-fold ( Figure 7C). Finally, with high cGAS cat and high ATP/GTP (the dimer population is significant), the differential activity caused by various dsDNA lengths was merely 1.5-fold, with short dsDNA molecules robustly activating cGAS cat ( Figure 7D). Furthermore, we observed the same trend from cGAS FL except the effect of raising substrate and enzyme concentrations was more pronounced than cGAS cat (Figure 7-figure supplement 1). These observations uncover the reason for conflicting observations regarding dsDNA length-dependence (Andreeva et al., 2017;Kranzusch et al., 2013;Li et al., 2013;Luecke et al., 2017). That is, the dependence on dsDNA length can either manifest or diminish by different reaction contexts that dictate the fraction of dsDNA-free cGAS dimers. Our results in turn indicate that cGAS is primed to generate a graded signaling output depending on the overall reaction condition (e.g. the length of cytoplasmic dsDNA, cGAS expression level, and available ATP/GTP), providing a molecular framework for its contextdependent and diverse stress responses (Gulen et al., 2017;Larkin et al., 2017;Li and Chen, 2018;Li et al., 2016;Tang et al., 2016)

Discussion
The activation of IFN-1 leads to diverse stress responses (antiviral gene expression, cellular senescence, autophagy, or apoptosis; (Gulen et al., 2017;Larkin et al., 2017;Li and Chen, 2018;Li et al., 2016;Liang et al., 2014;Tang et al., 2016;Yang et al., 2017)). cGAS contributes significantly to this complex signaling landscape by generating variable amounts of cGAMP (Li and Chen, 2018). Here, building upon the framework shown in Figure 2A, we set forth a unifying allosteric activation mechanism of cGAS, which explains how this cytoplasmic dsDNA sensor could dynamically tune its signaling activity in a switch-like fashion according to reaction (cellular) contexts ( Figure 7E). In this model, cGAS is subject to an intrinsic monomer-dimer equilibrium, with its N-domain potentiating the dimerization propensity. dsDNA can drive the monomer-dimer equilibrium toward the dimeric state, with duplex length determining the fraction of active dimers ( Figure 7E upper righthand path). Importantly, given the active unit of cGAS is a dimer, we propose that longer dsDNA simply increases the probability of forming dimers without invoking an ordered configuration. We also find here that cGAS allosterically couples its dimeric population to factors other than dsDNA, such as cGAS expression level and ATP/GTP availability ( Figure 7E, left path). We propose that this coupling mechanism would allow the dimer population to be in constant flux, providing a molecular framework for its dynamic signaling activity. Indeed, cGAS is subject to overexpression by multiple factors including its downstream product IFN-1 (Ma et al., 2015). Intracellular ATP/GTP concentrations also vary depending on cell age, cell-cycle progression, and stress conditions (Corton et al., 1994;Huang et al., 2003;Marcussen and Larsen, 1996;Traut, 1994;Wang et al., 2003). Moreover, post-translational modification (e.g. mono-ubiquitination) promotes dimerization of cGAS (Seo et al., 2018). Of note, given that pathogen infection increases host NTP levels (Chang et al., 2009;Ogawa et al., 2015), it is tempting to speculate that cGAS takes advantage of the higher intracellular NTP levels to increase its dimer population, potentiating its activation. Importantly, increasing the dimeric fraction in the absence of dsDNA would not elicit significant spurious activity, but would instead prime the enzyme for facile activation by reducing the dependence on dsDNA length ( Figure 7E lower left-hand corner). Another key feature of our equilibrium-based allosteric model is that dsDNA length-dependence is conditional, reconciling conflicting claims regarding the dependence on dsDNA length in activating cGAS (Andreeva et al., 2017;Gao et al., 2013b;Kranzusch et al., 2013;Li et al., 2013;Luecke et al., 2017;Zhang et al., 2014).

Molecular framework for the dsDNA length-dependent response of cGAS
As the initial receptor in a major inflammatory signaling pathway (Chen et al., 2016a), it is critical for cGAS to possess a very stringent noise filtering mechanism. Although cGAS binds dsDNA in a sequence-independent manner (Gao et al., 2013b;Li et al., 2013;Zhang et al., 2014), it uses dsDNA length to distinguish signal from noise (Andreeva et al., 2017;Luecke et al., 2017). After all, dsDNAs arising from catastrophic conditions are significantly longer than 300 bps (e.g. mitochondrial, genomic, and viral), while short dsDNAs likely indicate minor genome repair and/or resolution of infection (i.e. the viral genome has been degraded). Here, we find that the allosteric coupling mechanism allows cGAS to generate a two-stage noise filter against short dsDNA. For instance, as others have reported (Andreeva et al., 2017), we recapitulate here that cGAS binds and dimerizes on dsDNA in a length-dependent manner. Also as reported, we found that dsDNA length-dependent dimerization and binding of cGAS in vitro only gradually changes (Figures 2-4; Andreeva et al., 2017). However, we found that dsDNA length also grades the enzymatic activity of cGAS (Figures 3-4). Thus, combined with the length-dependent complex formation of cGAS dimers (signal recognition), the length-dependent enzymatic activity (signal transduction) would allow cGAS to further differentiate correct pathogenic dsDNA from noise (short dsDNA). Of note, given that dsDNA length-dependence subsides with high concentrations of cGAS, our new model also provides an avenue for how improper clearance of pathogenic or self-dsDNA can induce spurious activity of cGAS leading to auto-inflammatory conditions (Gao et al., 2015;Li and Chen, 2018).

The role of cooperativity in initiating and terminating the cGAS pathway
The interactions between cGAS and its ligands (dsDNA and ATP/GTP) display positive cooperativity, a hallmark of allosteric enzymes (Figures 2-4). One key feature of a cooperative system is its capacity to amplify and attenuate the output in a switch-like manner (Monod et al., 1965;Sohn and Sauer, 2009). For instance, when the concentrations of cGAS, dsDNA, and ATP/GTP change by a factor of two, a non-cooperative system would yield a total 8-fold increase in output (2 Â 2Â2=8). However, because cGAS requires dimerization for activity and displays a Hill constant near two in its interaction with both dsDNA and ATP/GTP, the same two-fold change would be further amplified by the exponent of two, leading to a 64-fold amplification in output (2 2 Â 2 2 Â2 2 =64). Conversely, the same cooperative mechanism would allow cGAS to attenuate its signaling output by the same magnitude with decreasing enzyme and ligand concentrations. Together with the dsDNA-length dependent activity, the cooperativity would enable cGAS to dramatically alter its output according to the changes in input parameters, allowing the initial receptor to dynamically regulate its signaling pathway in a switch-like manner. The role of N-domain and human vs. mouse cGAS Although cGAS cat is sufficient to bind dsDNA and generate cGAMP in vitro, the intact N-domain is crucial for augmenting its function in cells (Tao et al., 2017;Wang et al., 2017). It has been presumed that the major role of the N-domain is to enhance dsDNA binding (Lee et al., 2017;Tao et al., 2017). Furthermore, it was proposed that the N-domain promotes the activation of monomeric mouse cGAS by dsDNA (Lee et al., 2017). Here, we found that N-domain potentiates the dimerization of cGAS. Our results also indicate that dimerization is necessary for dsDNA-mediated activation by both cGAS cat and cGAS FL ( Figure 5). It is possible that mouse cGAS operates in a different mechanism than human cGAS. Indeed, it was recently proposed that mouse-cGAS would not depend on dsDNA length as much as human-cGAS for activation, as the former binds short dsDNA more tightly (Zhou et al., 2018). However, it was previously shown that both human and mouse-cGAS exhibit similar dsDNA length dependent activation (Andreeva et al., 2017). Considering that dsDNA-mediated dimerization is critical for both human and mouse cGAS variants for activation (Andreeva et al., 2017;Li et al., 2013;Zhang et al., 2014;Zhou et al., 2018), we propose that our findings are likely general phenomena across different species, and different intrinsic affinity constants caused by diverse primary sequences (Zhou et al., 2018) would dictate species-specific experimental observations.

Comparison with other nucleic acid sensors
Absent-in-melanoma-2 (AIM2) is another major cytoplasmic dsDNA sensor in mammals (Fernandes-Alnemri et al., 2009;Hornung et al., 2009;Roberts et al., 2009). The single most important goal of the AIM2-mediated dsDNA sensing pathway is to induce cell-death, a digital (not tunable) process that does not require a new equilibrium (Liu et al., 2014;Roberts et al., 2009). Indeed, once assembled on dsDNA, the AIM2 inflammasome does not disassemble and multiple positive feedback loops reinforce the assembly, consequently generating a binary signaling response (Matyszewski et al., 2018). By contrast, the cGAS signaling pathway elicits various stress-responses ranging from viral replication restriction to apoptosis, with the signal strength and cellular contexts determining the type of outcome (Gulen et al., 2017;Larkin et al., 2017;Li and Chen, 2018;Li et al., 2016;Liang et al., 2014;Tang et al., 2016;Yang et al., 2017). Unlike AIM2, we find here that cGAS can dial its own activity (tunable), providing a molecular framework for eliciting various cGAMP-dependent outcomes. Furthermore, although both AIM2 and cGAS are activated in a dsDNA length-dependent manner, the former assembles into filaments (Matyszewski et al., 2018;Morrone et al., 2015), while the latter only requires dimerization. Likewise, although cytoplasmic dsRNA sensors preferentially target long duplexes (>500 bps), MDA5 assembles into filaments while RIG-I does not require polymerization for activation (Linehan et al., 2018;Peisley et al., 2011;Peisley et al., 2013;Ramanathan et al., 2016;Sohn and Hur, 2016). Thus, we propose that the assembly of supra-structures is not universal to host nucleic acid sensors. Rather, it appears that each sensor has evolved unique mechanisms to utilize the length of nucleic acids as a molecular ruler to distinguish self (noise) from nonself (signal).
In closing, our study reconciles the conflicting views on the roles of dsDNA length and the N-domain in activating cGAS. We also provide a mechanistic framework for understanding how cGAS can shape a complex signaling landscape depending on cellular reaction contexts. Future studies will be directed in understanding how this dynamic enzyme operates in conjunction with its downstream and regulatory components to regulate host innate immune responses against cytoplasmic dsDNA.

Materials and methods
Reagents dsDNA substrates and oligonucleotides shorter than 100 bps were purchased from Integrated DNA Technologies (IDT). Longer dsDNAs (!150 bps) were generated by PCR. The human cGAS cDNA were kindly provided by Dr. Dinshaw Patel. E. coli pyrophosphatase was a gift from Dr. James Stivers. The SortaseA (SortA) enzyme was a gift from Dr. Hidde Ploegh. Purity and length of each dsDNA was confirmed by agarose gel electrophoresis. TAMRA-and Cy5-labeled peptides were purchased from Lifetein. ATP and GTP were purchased from Sigma. GMPcPP and AMPcPP were purchased from Jena Biosciences

Recombinant cGAS purification
Protein preparation. Recombinant cGAS constructs were cloned into the pET28b vector (Novagen) with an N-terminal MBP-tag and a TEV protease cleavage site. Proteins were expressed using 200 mM IPTG at 16˚C for overnight in E. coli BL21 Rosetta 2. Recombinant cGAS constructs were then purified using amylose affinity chromatography, cation-exchange, and size exclusion chromatography. Tag-free, purified cGAS proteins were then frozen and stored in À80˚C with a buffer containing 20 mM Tris HCl at pH 7.5, 300 mM NaCl, 10% glycerol, 5 mM DTT.

Biochemical assays
All experiments were performed at least three times. The fits to data were generated using Kaleidagraph (synergy). Reported values are averages of at least three independent experiments and report errors are standard deviations. All reactions were performed under 25 mM Tris acetate pH 7.4, 125 mM potassium acetate pH 7.4, 2 mM DTT, 5 mM Mg(acetate) 2 at pH 7.4, and 5% glycerol at 25 ± 2˚C.
dsDNA binding assays. Increasing concentrations of cGAS were added to a fixed concentration of fluorescein-amidite-labeled (FAM) dsDNA (5 -10 nM final). Changes in fluorescence anisotropy were plotted as a function of cGAS concentration and fit to the Hill equation. For competition-based experiments, unlabeled dsDNA was titrated against a fixed population of FAM-dsDNA 72 and cGAS ([protein] = K D,dsDNA72 ). Changes in fluorescence anisotropy (FA) was plotted against competitor dsDNA concentration and fit to yield IC 50 s.
FRET-based oligomerization assays. 60 nM Cy5-and TAMRA-labeled MBP-TEV-cGAS-LPET-GGGQC/K-fluorophore were incubated with TEV protease in cGAS reaction buffer at 25 ± 2˚C for 2 hr. Increasing amounts of dsDNAs of different lengths or equimolar concentrations of nucleotides were added to 20 nM cleaved FRET pair, and FRET efficiency was recorded until equilibrium was reached.
Pyrophosphatase-coupled cGAS activity assay. cGAS activity was assayed using the pyrophosphatase-coupled assay developed by Stivers and colleagues (Seamon and Stivers, 2015) with modifications. Briefly, cGAS was incubated with 50 nM E. coli pyrophosphatase, equimolar concentrations of ATP and GTP plus dsDNAs (where indicated) in the reaction buffer. At indicated time points, an aliquot was taken and mixed with an equal volume of quench solution (Reaction buffer minus Mg ++ plus 25 mM EDTA). Quenched solutions were then mixed with 10 ml malachite green solution and incubated for 45 min at RT. Absorbance at~620 nm was compared to an internal standard curve of inorganic phosphate to determine the concentration of phosphate in each well. Phosphate concentrations of control reactions devoid of recombinant cGAS were subtracted from reactions containing recombinant cGAS. Apparent catalytic rates were calculated from the slopes of control-subtracted phosphate concentrations over time. Reported rates were halved to reflect pyrophosphate production. Average values are listed in Tables.

SAXS data collection and analysis
SAXS data was collected on the BIOSAXS 2000 (Rigaku) at the X-ray facility of the Department of Biophysics and Biophysical Chemistry at Johns Hopkins School of Medicine. Data was collected on at least three different concentrations for each sample. SamplesBi with scatter showing significant inter-particle effects were omitted from data analysis. Buffer-subtracted scatter was processed in Scatter (Mylonas and Svergun, 2007;Petoukhov et al., 2012;Petoukhov and Svergun, 2013) and with the ATSAS package (Mylonas and Svergun, 2007;Petoukhov et al., 2012;Petoukhov and Svergun, 2013). Particle dimensions were compared between guinier analysis and real-space fitting of the scatter to ensure internal consistency of the data and fits. Estimates of average and relative molecular weights of each sample were estimated using porod volumes (Mylonas and Svergun, 2007;Petoukhov et al., 2012;Petoukhov and Svergun, 2013) and mass-normalized I 0 values. The distribution of monomeric and dimeric species was calculated using SAXS-estimated molecular weights and OLIGOMER. IN OLIGOMER, crystal structures of monomeric cGAS and dimeric cGAS were used as a reference (PDB ID: 4LEV).