PAR compaction and structural dynamics are influenced by cationic environmentTo build a comprehensive understanding of PAR’s conformational behavior in different environments, we performed explicit solvent MD simulations of PAR22 for a range of electrolyte conditions. A typical simulation began with the PAR polymer in a fully extended state, submerged in a 26 × 23 × 9 nm3 volume of electrolyte solution, a system of about 500,000 atoms (Fig. 2A). Upon energy minimization, each system was simulated for over 300 ns in the absence of any restraints using a CHARMM-compatible model of the PAR polymer (see “Methods” for details). Within the first 50 ns of equilibration, the polymer transitioned to a more compact state (Fig. 2B). The remaining 250 ns of each free equilibration simulation were characterized by computing the end-to-end distance (REE) and the radius of gyration (Rg) of the PAR polymer.Fig. 2: Molecular dynamics simulations of a 22-mer PAR polymer.A Initial configuration of a typical simulation system. One 22-mer PAR polymer is placed in electrolyte solution (semitransparent molecular surface) containing 50 mM of NaCl. B End-to-end distance (REE, in red) and radius of gyration (Rg, in blue) of a PAR molecule as a function of time simulated in 50 mM NaCl electrolyte. C, E, G Average equilibrium end-to-end distance (circles) and radius of gyration (squares) of the 22-unit PAR polymer at various ion conditions. Dashed lines connect the points to guide the eye. Each data point represents a 250-ns trajectory average after exclusion of the first 50 ns in each simulation where the molecule started in an extended state. Error bars denote S.D. from the average value. D, F, H Representative snapshots of PAR conformation at the end of a 300 ns equilibration performed at the specified ion concentration conditions. The O3′, C3′, C4′, C5′, and O5′ atoms of PAR are shown in green, whereas all other atoms are in blue. Na+ (yellow), Cl− (green) and Mg2+ (pink) ions located within 6 Å of PAR are shown as spheres. The ends of the PAR chains are depicted in red.Prior research, including circular dichroism analyses of mixed-chain length PAR molecules and our recent single-molecule Förster resonance energy transfer (smFRET) measurements, revealed that PAR compaction is sensitive to cations17,30. These findings align with established knowledge that nucleic acid structures are sensitive to their cationic environment31,32. In our MD simulations, we observed that both REE and Rg steadily decrease as the concentration of Na+ increases (Fig. 2C). Visualization of typical conformations indicates a transition: PAR adopts an extended, linear-like conformation at low salt concentrations and changes to a more compact, globular conformation at high salt concentrations (Fig. 2D). In the compact state, Na+ ions screened the backbone charge of PAR22, facilitating proximity between ADP-ribose units (Fig. 2D).We extended our simulations to examine the impact of Mg2+ on PAR conformation and found an extreme sensitivity to this cation (Fig. 2E). In this set of simulations, we kept the total charge of cations equal in magnitude to the charge of PAR22, while varying the fraction of the charge neutralized by Mg2+ from 0 to 100% (Fig. 2E, red points). Remarkably, increasing the fraction of charge neutralization by Mg2+ from 25 to 50% led to a two-fold reduction in REE. Further analysis revealed that Mg2+ ions do not compact PAR in a homogenous manner; instead, they induce the formation of highly compacted globules separated by extended polymer chains (Fig. 2F). This compaction was visualized over time across different systems using heatmaps that depict the number of neighboring ADP-ribose units within a 10 Å radius of each PAR residue (Supplementary Fig. 1). Counting the net charge within this radius over time further revealed the interplay between spatial localization and electrolyte charge compensation (Supplementary Fig. 2). Interestingly, the globular conformations observed at a neutralizing concentration of Mg2+ (100%, 7 mM) closely resemble those at much higher MgCl2 concentrations (50 mM). These data indicate that PAR22 is optimized for compaction even at Mg2+ concentrations much closer to physiological levels. This high sensitivity of PAR to Mg2+, including the formation of locally compacted domains (Supplementary Movies 1 and 2), suggests that Mg2+ may play a structural role. Beyond simply screening electrostatic charges, Mg2+ may trigger a transition of PAR from an elongated polymer to a condensed globule.To further quantify the effect of adding Mg2+, we conducted simulations with a fixed NaCl concentration of 50 mM while varying the MgCl2 concentration (Fig. 2G). These conditions align with those previously examined through smFRET experiments30. Our simulation showed that, in the presence of Mg2+, PAR transitioned from extended to compacted states and exhibited conformations where both states coexist within the same molecule (Fig. 2H, Supplementary Figs. S1, S2). When compared to simulations in pure NaCl solvent (Fig. 2C, D), the onset of compact conformations occurred at significantly lower MgCl2 concentrations. Specifically, a complete globular collapse occurred at 21 mM of MgCl2, in contrast to 2 M NaCl. Furthermore, over 39% of total compaction was achieved at a MgCl2 concentration as low as 3 mM. These observations are consistent with previous studies on single-stranded RNA, where only 5 mM MgCl2 was required to induce the same Rg change as 600 mM NaCl31.Taken together, our MD simulations show that PAR is structurally dynamic, adopting a range of conformations depending on the ionic environment. In the absence of Mg2+, PAR adopts extended conformations at physiological Na+ concentrations. However, even small amounts of Mg2+ can trigger local compaction of the PAR polymer—a structural transition that we further explored in the remainder of this study.SAXS reveals distinct compaction for PAR15 and PAR22 with Mg2+
Having surveyed a broad range of ionic conditions in the MD simulations of PAR, we focused on specific conditions for experimentally identifying various structural parameters of PAR using SAXS. We examined PAR15 and PAR22, both of which are found in normal and cancer cells, with the shorter one being more abundant24,25,26. The SAXS experiments were conducted in a 100 mM NaCl environment to approach physiological conditions, and we assessed the impact of adding 1 mM MgCl2 on PAR compaction.SAXS provides us with the overall size of the PAR structural ensembles, represented by the Rg values (Fig. 3A, B)33. In a 100 mM NaCl solution, PAR15 had an Rg of 24.4 ± 1.2 Å, while PAR22 had an Rg of 32.6 ± 0.5 Å (Fig. 3B). Adding 1 mM Mg2+ led to a 1.3 Å, or 5.3%, reduction in Rg for PAR15 and a larger 6.2 Å, or 19.0%, reduction for PAR22, indicating a greater compacting effect on the longer PAR22 molecule.Fig. 3: Length-dependent collapse of PAR polymer.A SAXS profiles of PAR15 and PAR22 in 100 mM NaCl with (red) and without (blue) the addition of 1 mM MgCl2. Data are plotted in dimensionless Kratky axes, normalizing out size differences and emphasizing changes in shape and disorder in the mid-angle scattering regime. Experimental scattering is shown in light-colored points, and solid lines show molecular form factor (MFF) model fits to the data, extracting the Flory scaling parameter ν (Supplementary Fig. 3)34. Error bars are derived from experimental error and rebinning. B SAXS-derived Rg values for PAR15 and PAR22 in the conditions assayed. Error bars show errors in the linear Guinier fits used to extract Rg. (Supplementary Fig. 4) C Radius of gyration of PAR15 and PAR22 polymers in MD simulations carried out at 100 mM NaCl, with and without 1 mM MgCl2. The histograms next to the timeseries plots illustrate the distribution of the Rg values. D Average simulated radius of gyration of PAR15 and PAR22 determined as a weighted mean ± square root of the weighted variance of the two Gaussian fit to the histograms. SAXS source data are provided as a Source Data file.We also calculated the Flory (ν) parameters for both PAR lengths at each salt concentration to understand their interaction with its surrounding solvent (Fig. 3A, Supplementary Fig. S3)34. Kratky plots were used for clearer data visualization, emphasizing the mid-angle scattering regime where the overall shape and degree of disorder of the molecular ensemble can be discerned35.When Mg2+ was absent, fits to SAXS profiles for both PAR15 and PAR22 yielded a ν value of 0.60 ± 0.02 and 0.60 ± 0.01, respectively. This ν value is expected for a self-avoiding random walk, suggesting similar polymer properties for both PAR lengths in a 100 mM Na+ environment. The ratio of Rg values between PAR22 and PAR15 (32.6 Å / 24.4 Å = 1.34) is consistent with the expected behavior for molecules with ν = 0.6, according to the classical scaling law, Rg α lengthν. This agreement provides additional confidence in this polymer description of PAR.When Mg2+ was introduced, PAR22 (ν = 0.55 ± 0.01) underwent a significant decrease in ν while PAR15 (ν = 0.59 ± 0.02) did not. These changes point to a stronger partial compaction of PAR22 (Fig. 3A, Supplementary Fig. S3). Overall, these experimental results indicate that the longer PAR22 undergoes a more significant conformational change when exposed to Mg2+ compared to its shorter counterpart, PAR15 (Fig. 3B).MD-SAXS reveals Mg2+ increases tortuosity and base stacking more in PAR22 than PAR15
To examine specific conformations in PAR responsible for the observed differences in size and shape, we integrated SAXS data with additional MD simulations. Specifically, we simulated the two PAR22 systems, both containing 100 mM NaCl electrolyte and differing by the presence of 1 mM MgCl2, for 1 µs each. In addition, we built and simulated, also for 1 µs each, two complementary PAR15 systems. All four systems contained about 160,000 atoms and initially occupied a volume of 12 × 12 × 12 nm3. During these simulations, we noticed that the PAR conformations transitioned between extended and compact states (Fig. 3C). Because of this bimodal behavior, and since the duration of simulation duration was comparable to the lifetime of each state, we were unable to determine the average Rg values for direct comparison (i.e., a large error margin when averaging Rg values across the entire simulations; Fig. 3D). As obtaining a microsecond duration trajectory of a 160,000 atom-system is, at the time of writing, at the practical limit of the MD methodology, we employed an ensemble optimization method (EOM) to refine the full pool of MD structures using SAXS data36,37. The computed scattering profiles from the refined ensembles closely matched the experimentally measured SAXS profiles in molecular shapes and overall Rg values (Figs. 4A, B, Supplementary Figs. S5, 6).Fig. 4: Determining structural ensembles for PAR using MD and SAXS.As an example, the case for PAR15 in 100 mM NaCl is shown. The same plots for PAR22 are shown in Supplementary Figs. 5, 6. A The pool of structures from the entire MD simulation is shown in orange, and the subset ensemble that agrees with the SAXS data in blue. Structures are parameterized in {Rg,REE} space. 1D histograms are weighted by the prevalence of each structure in the final ensembles. B Final agreement of the structural ensemble determined by EOM (blue) to the SAXS data (gray), compared to initial agreement of the structural ensemble of all MD conformers (orange). Gray error bars represent experimental errors. Residuals are shown in the bottom plot. C Ensembles of EOM-determined PAR structures, with and without Mg2+ for PAR15 and PAR22. Arrows show differential shifts to more compact states with the addition of Mg2+. D Tortuosities and E Fraction of adenine bases that are stacked in each structural ensemble of PAR, calculated as a weighted mean across the ensemble. For the tortuosity box-and-whisker plot in (D), the center mark is the medium and the box edges are the 25th and 75th percentiles; points outside the whisker edges are outliers (>2.7 S.D. from the mean). To gauge differences between groups, a two-sample two-sided t-test assuming unequal variances was performed, and ‘*’ denotes p < 0.05. Exact p-values: PAR15 100 mM NaCl vs PAR15 100 mM NaCl + 1 mM MgCl2: p = 0.1862, PAR22 100 mM NaCl vs PAR22 100 mM NaCl + 1 mM MgCl2: p = 5.969E-7, PAR15 100 mM NaCl vs PAR22 100 mM NaCl: p = 0.0027, PAR15 100 mM NaCl + 1 mM MgCl2 vs PAR22 100 mM NaCl + 1 mM MgCl2: p = 7.707E-11. For the base stacking plot in E, error bars show standard error. Number of structures in each refined ensemble: PAR15, 100 mM NaCl: 225; PAR15, 100 mM NaCl + 1 mM MgCl2: 563; PAR22, 100 mM NaCl: 75; PAR22, 100 mM NaCl + 1 mM MgCl2: 78. Note that, while the PAR15 pools have more unique structures, the weights of each structure are higher in the PAR22 pools (weights sum to 1000 in all pools).Next, we analyzed how PAR conformation and compaction change with Mg2+ for both PAR15 and PAR22 (Fig. 4C). The refined pools displayed a relatively uniform distribution of structures around an average, with no pronounced bimodality, as one would expect for a macromolecular ensemble (Supplementary Fig. 5). Importantly, the final fits between the EOM structural ensembles and SAXS data consistently fell within the experimental error margin, with ensemble Rg values in agreement across both methods (Supplementary Fig. 6). Supplementary Fig. 5 also lists the number of unique structures identified in each refined pool.With refined ensembles now available for all conditions (PAR15 and PAR22, both with and without Mg2+), we analyzed the included structures. We computed the tortuosity index of each structure in the identified ensemble to gauge their backbone conformations (Fig. 4D; see “Methods” for calculation method). Tortuosity quantifies how “twisted” the polymer is compared to a straight line connecting its endpoints. Without Mg2+, PAR22 has a significantly greater mean tortuosity across its structural ensemble than PAR15, indicating a more twisted backbone (Fig. 4D), despite the identical ν values. Interestingly, introducing Mg2+ significantly increased the tortuosity of PAR22, but not PAR15 (Fig. 4D).We also examined the role of π-π stacking in driving PAR chain compaction (Fig. 4E; see “Methods” for calculation method). Such interactions are particularly common among adenine bases and are known to induce intra-chain helicity in adenine-rich RNA sequences31. In the presence of 1 mM MgCl2, PAR15 underwent a 24% increase in base stacking events, whereas PAR22 exhibited a 103% increase (Fig. 4E). This greater frequency of π-π interactions between adenine bases could contribute to the greater compaction of PAR22 compared to PAR15.PAR22 displays ADP-ribose bundlesTo further analyze the structural ensembles revealed by EOM, we parameterized the structures according to their {Rg,REE} values and performed hierarchical clustering38. Using this approach, we found that the ensembles are highly heterogeneous: Rg and REE values covered 30 Å and 100 Å ranges, respectively. Through hierarchical clustering, we grouped structures into clusters with similar size, ranging from highly extended to highly compact (Supplementary Fig. 7).To elucidate unique conformational features within these clusters, we computed heatmaps of pairwise distances between bases in EOM-selected structure ensembles (Supplementary Fig. 8). These heatmaps revealed how ADP-ribose bases are connected along the PAR chains. In these maps, off-diagonal regions with shorter distance implies the crowding of distal bases. For PAR15, the heatmap revealed proximity mainly along the diagonal of the heatmap. This trend progressed monotonically toward the corners, suggesting that the molecule predominantly adopts relatively featureless extended conformations, irrespective of the presence or absence of MgCl2 (Supplementary Fig. 8A). In contrast, PAR22’s heatmap showed significant connections, or close contacts, between bases that are close together (blue regions, slightly off-diagonal). One such region appeared in the 100 mM NaCl map (upper left corner), while two were evident when 1 mM MgCl2 was added (upper left and lower right corners, Supplementary Fig. 8B). These off-diagonal regions indicate a local bundle of non-adjacent bases at the end(s) of the molecule, corroborating findings of local compaction initially identified in our MD simulations (Fig. 2).We next considered the role of π-π stacking in these distinct ensembles. For PAR15, regions of proximity (i.e., low inter-base distance) correlated somewhat with where base stacking occurs, mainly along the diagonals (Supplementary Fig. 8A). Yet, for PAR22, these off-diagonal low-distance regions were not enriched with base stacks (Supplementary Fig. 8B). Most stacking events occurred between adjacent bases along the chain. Thus, while PAR22 has more base stacking with 1 mM Mg2+ than PAR15 in general (Fig. 4E), the observed ADP-ribose bundles appear unrelated to base stacking. Rather, local chain compaction due to the proximity of the PAR phosphate backbone to an Mg2+ ion likely triggers the intra-chain coil-to-globule transitions that lead to these bundles. This transition is evident in individual frames of the MD simulations, where the compaction correlates to some extent with proximity of Mg ions to the backbone (Supplementary Fig. 9, Supplementary Movie 2). Taken together, our analyses on the heterogeneous structural ensembles confirm the presence of ADP-ribose bundle formation unique to PAR22.Distinct backbone conformations for PAR15 and PAR22
Hierarchical clustering partitioned the structural ensembles into groups based on the overall size of each structure; however, deriving a more concise description of the PAR backbone conformations was challenging due to a variety of poorly related structures populating in any size subgroup (Supplementary Fig. 7). Inspired by 2D classification of structures in single particle cryo-electron microscopy39, and graph theory, we grouped the ensembles into unique, interrelated conformational subclasses (Box 1). By applying 3D spatial alignment into network graphs and performing spectral clustering, we captured all conformations present in the ensembles, with no graph outliers (Supplementary Fig. 10). The low spatial variation between the constituent structures of these subclasses (Fig. 5 and Supplementary Fig. 11) supports that our algorithm effectively identified sensible classes, justifying the subsequent averaging to depict a single representative conformation in each class.Fig. 5: Backbone structural features of PAR15 vs PAR22 identified through spectral clustering.A–D PAR15 and PAR22 in 100 mM NaCl, both without and with the presence of 1 mM MgCl2, is shown. Top plots show the graphs of PAR structures in each ensemble, color-coded by the clusters identified by K-means. The box colors around each identified subclass match their locations in the graphs. Wireframe models show the mean PAR backbone conformation in each case—each dot represents the mean position of each pair of phosphorus atoms across the entire subclass, colored by the degree of spatial variance present across that class. Red squares denote the 1″ ends of the backbones and red triangles denote the 2′ ends. The fraction of each structural subclass within the entire ensemble is shown adjacent to the respective averaged backbone conformer models. E, F Proposed model of a critical length for coil-to-globule transitions in PAR in the presence of MgCl2, linking to previously observed differences in binding and condensing certain proteins16. Above a certain length, potentially between 15 and 22 subunits, PAR forms ADP-ribose bundles that impose super-anion functionality, accumulating negative charge and giving PAR a disproportionate amount of electrostatic potential. In longer PAR chains, these bundles may periodically appear along the chain, similar to the beads-on-a-string model of classical polymer theory.Without MgCl2 in 100 mM NaCl, the subclasses identified for PAR15 largely displayed similar conformations, with the backbone predominantly bent slightly into an inverted U shape (Fig. 5A). PAR22 exhibited similar U-shaped bends, but with additional variations: 21.3% of its conformations were more extended (Fig. 5B, green) and 16.0% more twisted (turquoise), likely contributing to the observed increase in tortuosity (Fig. 4E). Notably, bundles of ADP-ribose units were observed in PAR22 at the 1″ ends of each subclass (Fig. 5B), visually confirming our pairwise distance measurements between bases (Supplementary Fig. 8).The introduction of 1 mM MgCl2 accentuated the conformational differences between PAR15 and PAR22. The structural ensembles at 100 mM NaCl of both PARs were generally less connected, exhibiting greater distances between pairs of structures (Supplementary Fig. 10A, B). However, the presence of Mg2+ led to greater similarity among the structures within the ensemble, as evidenced by the increased number of structures demonstrating low root mean square deviations in pairwise comparisons (Supplementary Fig. 10C, D). Specifically, in PAR22, the occurrence of ADP-ribose bundles was now noted in all five of the identified subclasses, spanning those with extended and more compact conformations (Fig. 5D). This observation is consistent with the heatmap indicating an increase in the number of regions that have short pairwise distance between bases (Supplementary Fig. 8). The consistent low spatial variance (<20 Å) in these bundle regions across all subclasses further indicates the systematic presence of bundles throughout the structural ensemble (Fig. 5D). Each bundle contained ∼8 ADP-ribose units at each end, interconnected by 6 additional units.In contrast, such bundles were not present systematically enough in the PAR15 ensemble to be coherently observed with 1 mM MgCl2. These conformations closely resembled PAR15 in 100 mM NaCl alone, exhibiting similar backbone bending. A small fraction (4.6%) of the structures collapsed into a globule (Fig. 5C, yellow), akin to the most compact conformation observed in our initial MD simulations (Fig. 2). This subclass of collapsed globules may account for the slight 5.3% decrease in Rg in PAR15 as observed through SAXS (Fig. 3B). These data imply that only a small subset of molecules could undergo relatively featureless collapse with the small amount of Mg2+ present, leaving the rest of the ensemble relatively uninfluenced. On the other hand, the widespread bundling of the ADP-ribose units in PAR22 could explain the larger 19.0% decrease in its Rg (Fig. 3B). The difference in ADP-ribose bundle appearance alludes to a model of PAR’s length-dependent function (Fig. 5E, F).Box 1 Class averaging via spectral analysis of totally disordered macromolecules (CASA ToDiMo)Algorithm schematic.PAR has less helicity and base stacking than poly-adenosine RNAOur characterization of PAR and its distinct structural features prompted us to draw a comparison with poly-adenosine RNA. Though composed of the same ribose, phosphate, and adenine base building blocks, poly-A RNA and PAR have vastly different cellular functions. The former largely acts as a termination signal and binding motif, while the latter functions as a flexible binding scaffold. To delve into the structural difference between these two nucleic acids likely tied to their divergent functions, we compared a 15-mer of ADP-ribose (PAR15) to a 30-mer of AMP (rA30) RNA. Both molecules were measured with SAXS in identical solutions containing 100 mM NaCl. Because ADP-ribose (in PAR) contains twice the number of phosphate and ribose groups as AMP (in RNA), these two macromolecules have comparable length and overall charge. Their Rg values further affirmed their similarity (Fig. 6A). Importantly, we also chose PAR15 for comparison due to its lack of ADP-ribose bundles (Fig. 5), a feature not known to be present in poly-A RNA.Fig. 6: Polymeric differences of PAR15 vs poly-adenine RNA (rA30) in 100 mM NaCl.A SAXS-derived Rg of PAR15 vs rA30. Error bars represent errors in the Guinier fits. B Mean fraction of adenine bases that are stacked in the PAR15 and rA30 structural ensembles. C Ensemble-averaged orientation correlation functions of PAR15, compared to that of rA30. D Mean correlation lengths of PAR15 vs rA30, computed across the structural ensembles. E Four structures from the conformational ensemble of PAR15 that are most highly selected by EOM. F Four representative rA30 structures; accessible via SASDFB9 in the Small Angle Scattering Biological Data Bank31. Throughout this figure, blue refers to PAR15, and green refers to rA30. For (B–D), Error bars represent the variance in the datasets and are derived from analysis of N = 20 poly-A RNA structures (constituting the pool of structures from SASDFB9) and N = 225 PAR15 structures (constituting the pool of structures in the current study).The orientational correlation function (OCF) can describe the orientational alignment of local regions of a polymer chain as a function of the distance between its monomers (|i-j|). Peaks in OCF signify high periodic orientational directionality, while a featureless exponential decay represents random chain orientations40. Previous structural characterization of rA30 has revealed its well-ordered helix form, attributed to the propensity of adenine bases to undergo π-π interactions. The helix formation is driven by an extensive base stacking network, with 85.2 ± 2.5% of the bases adopting a parallel stacked configuration (Fig. 6B)31. The OCF of rA30 displayed strong oscillatory behavior with peaks spaced by the periodicity of an A-form helix (Fig. 6C). In contrast, PAR15 exhibited less orientational correlation along the chain, with the exponential decay of its OCF more closely resembled that of a random coil at |i-j| > 4 (Fig. 6C)40. This difference suggests that the bases in PAR are more randomly arranged than in RNA, supported by the mean PAR correlation length (6.1 ± 0.3 Å) being only a third of that of poly-A RNA (18.7 ± 0.2 Å) (Fig. 6D). The correlation length, which is greater when repeating backbone orientations are present, reflects the lower degree of order for PAR. Moreover, less than 14.4 ± 0.9% of the bases in PAR15 were stacked (Fig. 6B), preventing π-π interactions from stabilizing an ordered helical conformation, as is observed in rA30. The additional phosphate group and ribose sugar between each adenine base in PAR, compared to poly-A, may place the bases too far apart for extensive π-π base stacking interactions. Such differences in helicity and base stacking were evidently observed in individual sample conformers (Fig. 6E, F).
Cation-induced intramolecular coil-to-globule transition in poly(ADP-ribose)
