Abstract
CRISPR–Cas9 DNA cleavage requires R-loop extension to activate the histidine–asparagine–histidine (HNH) nuclease domain, yet how heteroduplex maturation gates catalytic commitment remains unclear. Using extensive molecular dynamics simulations across seven experimentally trapped heteroduplex states (6–18 nt), we define a three-stage activation pathway: unlocking, preorganization, and precatalytic gating. At the 18-nt checkpoint, HNH and REC2 regain mobility but do not adopt a fully cleavage-competent orientation; this dynamically frustrated metastate is consistent with a conformational-proofreading model. Here, dynamic frustration is used operationally to describe renewed mobility and weakened directional coupling without commitment to the cleavage-competent state, rather than a formal energetic frustration calculation. Two sensors, Y450 at the sgRNA: DNA hybrid interface and K1200 in the PI domain, respond to distinct maturation milestones, encoding heteroduplex length into domain-specific conformational outputs. Integrating these insights with two deep-learning analyses and deep mutational scanning recovers known high-fidelity positions and prioritizes three unannotated residues for testing. In a cellular cleavage reporter assay, R1210D reproduces the attenuated low-completion phenotype of eSpCas9, identifying it as a candidate for direct specificity testing, while destabilizing L1-linker substitutions increase cleavage efficiency. These results connect atomic-level dynamics to experimentally testable, structure-mechanism-informed engineering hypotheses; direct matched-versus mismatched validation is required to establish effects on discrimination fidelity.
Graphical Abstract
Graphical Abstract.

Introduction
Streptococcus pyogenes Cas9 (SpCas9, the prototypical CRISPR–Cas9 nuclease) mediates programmable DNA cleavage through a regulated, multistep target engagement pathway [1, 2]. Initial recognition occurs via interaction of the PAM-interacting (PI) domain with the protospacer adjacent motif (PAM) on the nontarget DNA strand (NTS). Base-pairing between the single guide RNA (sgRNA) and the target DNA strand (TS) then assembles the RNA:DNA heteroduplex, or R-loop [3, 4], which nucleates at the PAM-proximal seed region and propagates toward the PAM-distal end. Single-molecule studies have established PAM recognition and DNA unwinding as two kinetically distinct rate-limiting transitions; perturbations at either step, including guide-target mismatches, can stall the complex in nonproductive intermediates and abolish cleavage [5]. Consistent with this kinetic proofreading model, engineering the wedge domain of a thermostable Cas9 ortholog to accelerate unwinding enhanced editing efficiency over 100-fold [6], implying that R-loop formation kinetics are a central determinant of editing performance.
Among these kinetic gates, the extent of R-loop maturation is a primary signal governing commitment to cleavage. Cleavage requires two structurally distinct nuclease domains, histidine–asparagine–histidine (HNH) and RuvC, which cut the TS and NTS, respectively. Because HNH conformational activation is rate limiting for cleavage commitment and also allosterically licenses RuvC [7, 8], it constitutes a primary gate governing concerted double-strand cleavage. A fundamental question therefore remains: How is progressive R-loop extension transduced into the conformational signal that triggers HNH activation? Biochemical and structural studies have established a minimum hybrid length for efficient cleavage, a strong positional dependence of mismatch-induced inhibition [1, 9, 10], and large-scale HNH repositioning from a distal inactive conformation in the binary complex to a proximal precatalytic orientation in the ternary complex [11, 12]. Single-molecule Förster resonance energy transfer (FRET) further showed that HNH samples a dynamic equilibrium between docked and undocked states, exquisitely sensitive to the length and integrity of the RNA:DNA hybrid [7, 13]. Complementary large-scale molecular dynamics (MD) simulations and Markov state modeling by Lu et al. described a gear-and-wedge mechanism involving the L1 folding, L2 rearrangement, REC2 displacement, and transient REC2-HNH contacts during HNH activation [14]. Together, these findings establish HNH activation as a kinetically gated, multistep process conformationally coupled to R-loop maturation.
Cryo-EM has begun to resolve these intermediates: Pacesa et al. [15] captured seven discrete structures spanning R-loop lengths from 6 to 18-nucleotide (nt) at 2-nt intervals, revealing stepwise conformational changes including REC2 and REC3 remodeling, L1/L2 linker restructuring, and HNH translocation toward the TS, and proposing the 18-nt state as a precatalytic checkpoint. However, cryo-EM provides static snapshots of the dominant conformation at each length and cannot resolve the underlying dynamic ensemble, quantify the spatial distribution of conformational reorganization, or map the allosteric pathways that transmit information from R-loop growth to nuclease activation.
MD simulations provide dynamic complement to static structures. Prior all-atom MD has illuminated HNH docking and the role of the NTS in stabilizing the competent state [16], the allosteric role of PAM through L1/L2 linkers [17], and the mechanism by which PAM-distal mismatches immobilize HNH [18]. Combined nuclear magnetic resonance (NMR) and MD identified a millisecond dynamic pathway from the RuvC interface through HNH to REC2 [19], and subsequent work showed that high-fidelity variants disrupt this pathway in proportion to their specificity gain [20], while diverse PAM-distal perturbations converge on HNH immobilization [21]. Nevertheless, these studies largely compared endpoint states or isolated perturbations, leaving unresolved whether R-loop maturation traverses a continuous landscape or passes through discrete, mechanistically distinguishable stages, a distinction with direct implications for how fidelity is encoded.
Here, we show that R-loop propagation in SpCas9 from 6-nt to 18-nt proceeds through a discrete three-stage allosteric program of unlocking, preorganization, and precatalytic gating, and that the apparent stability of the 18-nt checkpoint masks an underlying dynamic frustration. We use this term operationally for the near-precatalytic HNH arrangement in which HNH and REC2 regain mobility while directional coupling weakens, so the ensemble samples without committing to the cleavage-competent state; it does not denote a formal energetic-frustration calculation. Using 35 μs of all-atom MD simulations across seven trapped R-loop intermediates [15], we identify structural switch residues enriched in the RuvC-III subdomain and L1 linker, and two sensor residues, Y450 at the sgRNA interface and K1200 in the PI domain, that monitor distinct functional transitions. Combining MD simulations with two complementary deep-learning analyses and an independent deep mutational scan recovers established high-fidelity positions and nominates three uncharacterized residues, Y271, R1210, and L625, for testing. In a cell-based cleavage reporter, R1210D in the PI domain reproduces the attenuated low-completion phenotype of eSpCas9(1.1) [22], making it a candidate for direct specificity testing, whereas substitutions in the L1 linker increase activity. Together, these results convert a dynamic, testable model of conformational proofreading into experimentally supported engineering nominations.
Materials and methods
Structural modeling
Seven SpCas9/sgRNA/DNA ternary complexes spanning 6–18 nt of guide–target hybridization were built from the cryo-EM models of Pacesa et al. [15] (PDB IDs: 7Z4C, 7Z4E, 7Z4K, 7Z4G, 7Z4H, 7Z4I, 7Z4L). Because several models contain unresolved internal loops and missing nucleotides, we restored these regions using AlphaFold3 [23] predictions superimposed onto the cryo-EM scaffolds in PyMOL [24], transferring only the conformers most compatible with the flanking resolved density. All experimentally resolved coordinates were preserved; rebuilt segments are small, solvent exposed, and equilibrate rapidly in MD.
A dedicated modeling decision governs the 12-nt intermediate, where HNH is invisible or only residually resolved in the cryo-EM maps, consistent with its high rigid-body mobility at intermediate R-loop lengths [15]. Rather than predicting a de novo HNH pose, we grafted the 14-nt undocked HNH (7Z4H) into the 12-nt state after superposition of the L1 and L2 linkers, reasoning that the 14-nt undocked pose is a more faithful representative of mobile intermediate HNH than the 10-nt repositioned state. Grafting validity was confirmed by HNH backbone root-mean-square deviation (RMSD) across five replicas (Supplementary Fig. S1): The absence of sustained drift or unfolding demonstrates that HNH tertiary structure is preserved, while the large rigid-body excursions responsible for the low cryo-EM local resolution manifest instead in the per-residue root-mean-square fluctuation (RMSF) analysis reported below.
Interpretation of R-loop state series
The seven R-loop states modeled in this study (6-, 8-, 10-, 12-, 14-, 16-, and 18-nt; PDB ID: 7Z4C, 7Z4E, 7Z4K, 7Z4G, 7Z4H, 7Z4I, 7Z4L) correspond to kinetically trapped intermediates captured by Pacesa et al. [15] using PAM-distal mismatched substrates. These structures represent pseudoequilibrium snapshots of discrete checkpoint states rather than uniformly spaced points along a continuous reaction coordinate: The 2-nt intervals reflect experimental substrate design, and each state is stabilized by a distinct mismatch pattern that may introduce local perturbations to duplex geometry and PAM-distal protein contacts. Because mismatch identity covaries with nominal R-loop length, the series cannot by itself separate effects of extension from substrate-specific effects; in particular, the 16-to-18-nt difference may contain both contributions. Accordingly, all network and dynamical analyses treat each state as an independent structural ensemble. Interstate comparisons are performed between adjacent states and interpreted qualitatively; no linear interpolation, smoothing, or continuous reaction-coordinate assumption is applied. Nonmonotonic features, including HNH/REC2 reloosening at 16–18 nt, are therefore reported as state-resolved observations that motivate, rather than prove, the checkpoint model.
Molecular dynamics simulations
Simulations of SpCas9 (1368 residues) were performed using pmemd.cuda from Amber24 [25] with protein described by ff19SB [26], RNA by OL3 [27], DNA by bsc1 [28], water by TIP3P [29], and ions by the Joung–Cheatham set [30]. Each of the seven R-loop states was propagated as five independent 1 µs replicas in the NPT ensemble at 300 K and 1 atm with a 2 fs timestep, SHAKE on bonds to hydrogen, and particle mesh Ewald (PME) electrostatics (10 Å cutoff). Trajectory frames were saved every 10 ps, yielding 35 µs of cumulative sampling. Sampling convergence was assessed by block-averaged ΔRMSF across replicas. Replica redundancy was chosen to ensure statistical convergence of the slow 12-nt to 18-nt checkpoint dynamics that motivate this study. Routine system preparation (protonation assignment, solvation, and neutralization) and the two-stage minimization, NVT heating, and NPT equilibration protocol are detailed in Supplementary Note 1.
Principal component analysis
To resolve the collective transitions bridging adjacent hybridization states, principal component analysis (PCA) was performed on concatenated trajectories from each pair of consecutive states (6/8, 8/10, 10/12, 12/14, 14/16, 16/18-nt) using domain Cα covariance matrices. The leading eigenvector (PC1) was rendered as porcupine plots in VMD [31], and structures were visualized in VMD and PyMOL. Domain boundaries follow the canonical SpCas9 architecture [3, 15] with L1 and L2 treated as separate functional units per Huai et al. [12] and Palermo et al. [32] (Supplementary Note 1).
Differential flexibility analysis
Per-residue backbone RMSF was computed with gmx rmsf [33] against the time-averaged structure. Differential RMSF between consecutive states (ΔRMSF = RMSFn+1 − RMSFn) was summarized at the domain level using the median rather than the mean, limiting domination by high-amplitude solvent-exposed loops and emphasizing concerted shifts of the structured core. The ± 0.2 Å cutoff was used as an operational effect-size threshold for classifying domain-level changes, not as a universal physical boundary. A sensitivity analysis over 0.15–0.30 Å retained the central stage-defining pattern: REC2/HNH rigidification at 14-to-16 nt followed by reloosening at 16-to-18 nt.
Secondary structure classification
Secondary structure was assigned per frame with DSSP [34] and reduced to a binary structured (α/β) versus disordered (coil, turn, bend) label. A residue was classified as a structural switch if the maximum pairwise difference in structured occupancy between any two of the seven states exceeded 40%, a cutoff chosen to reject thermal noise while capturing genuine state-dependent remodeling. Switches were partitioned by their monotonicity along the 6- to 18-nt axis into folders (net disorder-to-order), melters (net order-to-disorder), and transient (nonmonotonic).
Interaction network analysis
Salt bridges, hydrophobic contacts, and hydrogen bonds were scored per trajectory using standard geometric criteria in MDanalysis [35, 36] (details in Supplementary Note 1). To correlate transient noncovalent interactions with the functional progression of R-loop maturation, per-residue occupancy vectors were thresholded (0.50 for salt bridges, 0.40 for hydrophobic contacts), constitutive interactions (present in all seven states) were excluded, and the remaining dynamic interactions were assigned to seven mutually exclusive overlap categories across three analytically defined stages: Stage 1 (6-nt to 10-nt, unlocking), Stage 2 (10-nt to 14-nt, preorganization), and Stage 3 (14-nt to 18-nt, precatalytic gating). Because the seven cryo-EM models carry slightly different DNA sequences and hybridization lengths, we imposed a spatially aligned, sequence-agnostic nucleotide numbering so that equivalent positions share identical indices across states (details in Supplementary Note 1).
Dynamical network and community analysis
Dynamical networks were constructed for each state following the Nierzwicki pipeline [19, 20]: nodes are residues 1–1368; edges connect pairs whose heavy atoms sit within 4.5 Å in ≥ 75% of frames. Generalized cross-correlation matrix (GCCM) elements quantify correlated residue motions using the Lange–Grubmüller estimator [37]. Their magnitudes were converted to edge impedances, wij = −ln|Cij| [38], so strongly correlated pairs form low-impedance communication paths. Taking the absolute value allows concerted and opposing motions to serve as equally effective mechanical-signal conduits.
Community structure was resolved by weighted Girvan–Newman edge-betweenness decomposition [39, 40] using GCCM-derived impedance weights. Edges were removed iteratively according to weighted edge betweenness, and the partition with maximum modularity along the resulting dendrogram was retained for each state. Louvain optimization [41] was not used for the reported communities. Modularity scores [39] Q = 0.79–0.82 across all states (Supplementary Fig. S2B) describe the separation of the recovered dynamical modules. Weighted node betweenness centrality [42] identified bottleneck hubs.
Suboptimal paths were enumerated with Yen’s K-shortest paths algorithm [43] (K = 10) across twelve source–sink pairs in four diagnostic groups: Group 1, REC3 α37 (692, 694, 695, 698) to HNH catalytic residue 840, a literature-validated control [19, 20]; Group 2, REC/HNH interface (789, 794) to the HNH/RuvC interface (841, 858), recapitulating the classical hinge route; Group 3 (novel TS sensor), Y450 to residues 840 and 10; Group 4 (novel NTS displacement probe), K1200 to residues 840 and 10. Groups 1 and 2 anchor the analysis against established routes; Groups 3 and 4 interrogate the sensors identified in this work. Adjacent-state GCCM differences were assessed by bootstrap resampling (N = 1000; 95% confidence intervals and pairwise P-values reported). Networks were implemented in Python 3.12 with NetworkX [44].
AI-based substitution-intolerance and conformational-selectivity analyses
To evaluate the MD-derived allosteric residue set with different model inputs, we used two complementary deep-learning analyses. First, Variant Effect Score Model (VESM) [45] (an ESM2-3B backbone loaded with VESM distilled weights) scored each substitution by masked-marginal log-likelihood ratio and summarized each position as sign-inverted mean log-likelihood ratios (LLRs) (−meanLLR). This quantity is interpreted as model-inferred substitution intolerance from learned protein-sequence patterns, not direct evolutionary conservation. Second, conformational bias (CB) analysis with ProteinMPNN [46, 47] measured structure-conditioned sequence compatibility across the seven R-loop backbones and yielded a state-directional conformational-selectivity score (−ZCB,bias) from transition-wise log-probability differences. CB is not a physical energy or a substitution-fitness predictor. Full parameters, normalization protocols, and flipper-residue classification are detailed in Supplementary Note 2.
A composite MD score (PMD) was constructed from five nonredundant dynamical categories: structural switch (84 residues), GCCM variance (54), salt-bridge partner switching [46], hydrophobic partner switching (90), and peak betweenness centrality (89); category definitions and elbow-derived cutoffs are given in Supplementary Note 3. The union contains 311 MD-annotated residues. The final stringent MD key-residue set comprises the 52 residues supported by at least two independent categories (Hub_Overlap_Count ≥ 2), designated superhubs; thus, the centrality elbow at k = 89 is a category-specific cutoff, not the final key-residue count. Integrated scores combined PMD, PVESM, and PCB as an equally weighted percentile mean, with an evidence count (0–3) tallying how many methods placed a residue above the 50th percentile. A median-split partition of CB driving force against VESM substitution intolerance yielded Q1 core drivers, Q2 functional invariants, Q3 background, and Q4 plastic drivers. Within each quadrant, residues were ranked first by Hub_Overlap_Count and then by the quadrant-discriminating axis (substitution intolerance for Q1/Q2; CB for Q3/Q4).
To test this partition’s predictive validity, we cross-referenced against the Spencer and Zhang deep mutational scanning [48] (2470 observations across 1185 positions; 2346 matched at substitution resolution). All domain annotations were remapped to the 12-domain boundaries used throughout this study. Method independence and predictive power were confirmed at substitution resolution using Kruskal–Wallis testing, partial Spearman correlations, and cross-validated ROC analysis (statistical derivations and power calculations in Supplementary Note 2). Triple-convergent Q4 engineering candidates were defined as residues satisfying: MD superhub status (Hub_Overlap_Count ≥ 2), DMS tolerance (median log2FC > 0), and high CB driving force. Analyses were implemented in Python 3.12 (NumPy, SciPy, Pandas, MDAnalysis, NetworkX, scikit-learn) with custom pipeline scripts.
Plasmid construction and reagents
To express SpCas9 in Escherichia coli, the SpCas9-encoding cDNA was obtained from Saiheng Biological Technology (Shanghai, China) and cloned into the pET28a expression vector bearing an N-terminal hexahistidine (His6) tag. Site-directed mutagenesis of the wild-type SpCas9 coding sequence was performed to generate a panel of 19 variants, comprising 18 single-residue substitutions (Y271A, Y271D, Y271F, R1210A, R1210Q, R1210D, L625A, L625D, Q771A, K772A, A538G, A1034G, F1037A, Y1242A, M495A, R925A, K961A, and V1018D) together with the previously described high-fidelity eSpCas9(1.1) construct, which harbors the K848A, K1003A, and R1060A substitutions and was included as a benchmark for comparison. Mutagenesis was performed using the Mut Express II Fast Mutagenesis Kit V2 (Vazyme Biotech, Nanjing, China), and all mutations were verified by Sanger sequencing (Personalbio, Shanghai, China).
For mammalian cell experiments, the coding sequences for SpCas9, the sgRNA, and the sgRNA target site (with its PAM) positioned between the 5′ fragment (GF) and the 3′ fragment (FP) of the split-GFP reporter were synthesized by Saiheng Biological Technology and assembled into pCMV or pBFP backbones by Golden Gate cloning.
Cell culture and transient transfection
HEK293T cells were maintained in Dulbecco’s modified Eagle medium supplemented with 10% fetal bovine serum (FBS) at 37°C in a humidified 5% CO2 atmosphere. Approximately 24 h before transfection, cells were dissociated with trypsin and seeded into 24-well plates at a density of 1.0 × 105 cells per well. At ∼60% confluence, cells were cotransfected with a total of 1 µg of plasmid DNA per well, comprising 0.7 µg of the appropriate SpCas9/sgRNA construct (wild type or mutant) and 0.3 µg of the GF × FP reporter plasmid, using 2 µl of ExFect transfection reagent (Vazyme Biotech) according to the manufacturer’s instructions. Co-delivery of the nuclease and reporter plasmids ensured that GFP fluorescence directly reflected the cleavage activity of the corresponding construct. Cells were harvested at 24, 48, and 72 h posttransfection for downstream analysis.
Flow cytometry and cleavage quantification
Reporter activation was quantified by EGFP fluorescence on a CytoFLEX flow cytometer (Beckman Coulter). The GF × FP reporter remains nonfluorescent until a SpCas9-induced double-strand break between the GF and FP fragments triggers single-strand annealing, reconstituting a functional GFP cassette; consequently, the percentage of GFP-positive cells provides a direct readout of on-target cleavage activity. Gating was performed on the FITC channel versus side scatter to identify GFP-positive events, which were further stratified into GFP-low and GFP-high populations according to predefined fluorescence intensity thresholds. The GFP-high fraction was interpreted as cells that had undergone robust reporter repair. For each construct, the total GFP-positive percentage and the GFP-low and GFP-high subfractions were recorded at each time point.
To capture the depth of editing at a fully matched target site, we defined an editing completeness index as the ratio of the GFP-high fraction to the total GFP-positive population. This metric reflects editing efficiency independently of off-target discrimination. Baseline fluorescence was established using untransfected cells and cells transfected without sgRNA, and the wild-type SpCas9 construct was included in every experiment as an internal activity reference.
Statistical analysis and reproducibility
All flow cytometry assays were performed across three independent biological replicates. Data are presented as the mean of these replicates, with error bars denoting the standard error of the mean. Sample sizes were not predetermined by statistical methods, and no data points were excluded from the analysis.
Results
R-loop extension drives a three-stage allosteric trajectory
The domain architecture of SpCas9 is summarized in Fig. 1A. The sgRNA initiates base-pairing with the TS at the seed region and progressively extends the heteroduplex across seven resolved states from 6-nt to 18-nt at 2-nt intervals (Fig. 1B, C). To characterize how this extension reshapes the nucleic acid core and the protein scaffold, we performed all-atom MD simulations on cryo-EM-derived SpCas9-R-loop complexes for each intermediate, running five independent 1-us replicas per state (35 μs cumulative).
Figure 1.

R-loop formation during progressive DNA binding by the SpCas9–sgRNA complex.(A) Domain organization of SpCas9 with color-coded domains. (B) Schematic of SpCas9–R-loop complexes with progressively extending guide–target complementarity from 6 to 18 nt at 2-nt intervals. (C) Structural comparison of representative SpCas9–R-loop complexes across the seven R-loop states (PDB ID: 7Z4C, 7Z4E, 7Z4K, 7Z4G, 7Z4H, 7Z4I, 7Z4L for 6-, 8-, 10-, 12-, 14-, 16-, and 18-nt states, respectively), shown as surface representations with domains highlighted by color.
Across seven states, the expanding heteroduplex imposes progressively increasing spatial constraint within the nucleic acid binding channel. The distal DNA duplex kinks from a near-linear geometry at 6 nt to a sharply bent conformation at 10 nt and beyond (Fig. 1C; Supplementary Fig. S3), consistent with prior structural studies [11, 49], while the NTS is progressively displaced and extruded, culminating in a solvent-exposed single-stranded loop at 18 nt. To resolve the scaffold response, we performed PCA on concatenated trajectories spanning adjacent states and extracted the dominant principal component 1 (PC1) for each pairwise transition (Fig. 2). The porcupine plots reveal an ordered three-stage trajectory, comprising unlocking, preorganization, and precatalytic gating, which we propose as the unifying framework governing SpCas9 activation during R-loop propagation.
Figure 2.

Progressive conformational dynamics and collective domain translocations of SpCas9 driven by R-loop extension. PC1 porcupine plots for the six stepwise transitions 6-nt→8-nt, 8-nt→10-nt, 10-nt→12-nt, 12-nt→14-nt, 14-nt→16-nt, and 16-nt→18-nt, derived from PCA of concatenated MD trajectories for each pair of adjacent states. Arrow direction indicates the direction of motion along PC1; arrow length scales with displacement magnitude. PC1 captures the largest single component of variance across each pairwise trajectory. Three stages are delineated: Stage 1 (6-nt to 10-nt, unlocking; DNA bending and initial domain accommodation), Stage 2 (10-nt to 14-nt, preorganization; latent unidirectional REC2 drift), and Stage 3 (14-nt to 18-nt, precatalytic gating; HNH repositioning and checkpoint).
During unlocking (6–10 nt), REC2, REC3, and HNH undergo coordinated repositioning that tracks the kinking of the distal duplex. During preorganization (10–14 nt), collective motion becomes spatially focused: only REC2 exhibits appreciable displacement, drifting unidirectionally away from the R-loop core. This latent drift is not resolvable from static cryo-EM and emerges only from ensemble-averaged dynamics, representing a preparatory step in which directional strain accumulates while the global architecture remains superficially stable. Precatalytic gating (14-nt to 18-nt) shows the most dramatic behavior. At the 14-to-16-nt transition, REC2, REC3, RuvC, and HNH execute a large-scale anticlockwise repositioning, with HNH showing the largest movement toward the TS scissile phosphate and the largest PC1 magnitudes across the trajectory. The subsequent 16-to-18-nt transition shows no detectable large-scale motion, consistent with smFRET data indicating that HNH adopts a metastable docked conformation distinct from the active state [13].
A dynamically frustrated checkpoint emerges at the 18-nt state
We next asked where the flexibility changes at each transition are spatially concentrated, computing per-residue ΔRMSF profiles aggregated into 12 SpCas9 domains (Fig. 3A; Supplementary Fig. S4; Supplementary Table S1), classifying each domain as loosening (ΔRMSF > +0.2 Å), rigidifying (ΔRMSF < −0.2 Å), or stable. During the 6–8-nt transition, REC3 (+0.537 Å) and L2 (+0.401 Å) loosen to accommodate the nascent hybrid, while the L1 linker undergoes early, pronounced rigidification (−0.400 Å), foreshadowing its role in long-range communication. The 14-to-16-nt transition is the most dramatic step, with near-global rigidification across REC1-A, REC1-B, REC2 (−0.517 Å), HNH (−0.872 Å), and PI. The HNH value (−0.872 Å) is the largest ΔRMSF across the trajectory and coincides with the large-scale HNH repositioning seen by PCA, indicating that HNH becomes conformationally locked into a precatalytic orientation.
Figure 3.

Dynamic landscape and allosteric role assignment during SpCas9 activation.(A) Surface representations of SpCas9 showing localized ΔRMSF values between adjacent intermediate states. Blue indicates regions undergoing significant loosening (ΔRMSF > +0.2 Å); red highlights significant rigidification (ΔRMSF < −0.2 Å). (B) Clustering of domain-specific mean RMSF trajectories across the 6-to-18-nt R-loop extension process, classifying domains into three functional modules: the static rigid scaffold, the sensors and transducers allosteric network, and the HNH catalytic payload.
The 16-to-18-nt transition breaks this pattern. REC2 (+0.442 Å) and HNH (+0.483 Å), both maximally rigidified at the previous step, undergo abrupt, large-magnitude reloosening. This localized surge in flexibility, occurring while the system is poised near the precatalytic state, marks a dynamically frustrated checkpoint: HNH is sterically primed near the scissile phosphate but lacks the directional coupling required for catalytic commitment. We use “frustration” here in a kinetic-gating sense rather than the energetic-landscape sense of Ferreiro et al. [50]. Domain-level clustering of RMSF trajectories places this within three dynamical modules (Fig. 3B; Supplementary Table S1): a Rigid Scaffold (REC1-A, REC1-B, RuvC-I, RuvC-II, BH, PI) maintaining integrity across the window; a sensors and transducers network (REC2, REC3, L1, L2, RuvC-III) undergoing progressive remodeling; and the catalytic payload (HNH), which integrates upstream signals and is primed toward the docked conformation. The correlated reloosening of HNH and REC2 at 16-to-18-nt indicates that the catalytic payload remains responsive to ongoing remodeling of the sensors module, leaving HNH in a metastable intermediate within the gating phase.
Secondary structure remodeling concentrates in RuvC-III and the L1 linker
To resolve where local conformational reorganization accumulates, we computed time-averaged secondary structure occupancy for all residues across seven states (Fig. 4A). Most residues (>800) maintain stable secondary structure, consistent with the rigid scaffold, while a small subset shows transition-coupled remodeling. We define structural switch residues as those with a maximum occupancy shift exceeding 40% across any pairwise transition, classified by directionality: Folders transition disorder-to-order, melters order-to-disorder, and transient residues undergo nonmonotonic shifts. Eighty-four residues satisfy the criterion and distribute asymmetrically: RuvC-III is overwhelmingly enriched with 41 residues (∼49%), followed by REC2 [11], PI [10], REC3 [8], L1 [6], RuvC-I [6], and REC1-B [2] (Fig. 4B, C; Supplementary Table S2).
Figure 4.

Global secondary structure dynamics and identification of structural switches during SpCas9 activation.(A) Heatmap of time-averaged secondary structure order (% time in α-helix or β-strand) for all SpCas9 residues across the 6-to-18-nt states. (B) Histogram of maximum secondary structure shifts, with residues classified into stable core (<15%), flexible (15%–40%), and structural switches (>40%). (C) Stacked bar chart showing domain distribution and transition trends (folders, melters, transient) of the 84 structural switch residues.
Within RuvC-III, these residues partition into a central order-gaining cluster flanked by two disorder-gaining clusters, forming a locally segregated pattern rather than uniform remodeling (Supplementary Fig. S5). The central Folder cluster (residues 1024–1028) establishes close TS contacts at 18 nt, suggesting that local folding is coupled to DNA positioning as the R-loop approaches full extension. Per-residue force analysis showed that full R-loop engagement does not stabilize RuvC-III uniformly but redistributes order within it: the same mechanical input at 16-to-18-nt drove folders from order to disorder and Melters in the opposite direction (Supplementary Fig. S6; Supplementary Note 3). L1 hosts a second high-density switching region, with six of seven consecutive residues (769–775) qualifying as switches in a bipartite arrangement, three Folders (769, 771, 772) at the N-terminal side and two Melters (774, 775) at the C-terminal side, complementing the early L1 rigidification seen in the ΔRMSF analysis. Switch-residue distributions in REC2, REC3, and PI are detailed in Supplementary Note 3 and Supplementary Table S2.
State-dependent interaction network rewiring couples R-loop maturation to HNH repositioning
The inter-residue contact network rewires progressively across R-loop progression. To isolate interactions that actively change state, we converted occupancy vectors into binary presence/absence profiles and analyzed the dynamic subset of salt bridges and hydrophobic contacts (Supplementary Tables S3 and S4). Residue-level tracking reveals extensive partner switching rather than simple gain or loss, with individual residues frequently terminating in a different state from the one in which they first appear (Fig. 5A). The net flux of salt-bridge-forming residues is nonmonotonic (Fig. 5B), with bursts of formation at 6-to-8-nt and 14-to-16-nt offset by net losses at 8-to-10-nt and 16-to-18-nt.
Figure 5.

Dynamics of salt-bridge residues during progressive R-loop formation in the SpCas9–sgRNA complex.(A) Sankey diagram of salt-bridge residue state transitions from 6-nt to 18-nt. (B) Bar and line plots of persisting, disappearing, and appearing salt-bridge residues and net flux at each transition. (C) Inter-domain salt-bridge diagrams, with edge thickness proportional to the number of contacts. (D) Representative salt-bridge residues.
The HNH–TS and RuvC–NTS interfaces dominate the protein–DNA salt-bridge landscape (Fig. 5C), becoming more prominent as the R-loop matures and reporting specifically on state-gated engagement of the cleavage domains with their cognate strands. At the L1 and RuvC-III regions, positively charged residues (K1200, R925, R895; Fig. 5D) engage multiple nucleic-acid partners in a state-specific manner. K1200 exemplifies this most clearly: Its NTS salt-bridge partner shifts progressively from NTS1522 (6-, 8-nt) to NTS1524 (10-, 12-nt), NTS1526 (14-nt), NTS1528 (16-nt), and NTS1530 (18-nt), advancing approximately one backbone position per 2-nt increment. This stepwise sliding contact couples K1200 to the retreating NTS backbone, positioning it as a candidate sensor that tracks R-loop maturation in register with heteroduplex extension. Hydrophobic contacts undergo a parallel but distinct remodeling around a state-gated L2-RuvC axis, while constitutive interactions form a stable REC1/PI scaffold (Supplementary Note 4; Supplementary Figs S7–S10). Two constitutive junction contacts are notable exceptions (Supplementary Figs S10 and S11): F405 maintains persistent TS contact as a duplex anchor and Y450 maintains continuous sgRNA contact throughout maturation (occupancy 0.77–0.98), base stacking with the seed-proximal sgRNA nucleotide at 6 nt and unstacking at 8 nt to permit extension [15], while preserving hydrophobic contact thereafter, a transition from stacking gatekeeper to persistent anchor.
Dynamical network analysis identifies Y450 and K1200 as candidate sensor residues
To map long-range communication, we constructed residue-level dynamical networks for each state using generalized cross-correlation matrices (GCCMs) [37], whose elements quantify correlated residue motions, and converted the correlation magnitudes into edge impedances (Fig. 6). Global coupling intensity across all 1368 residues peaks sharply at 8 nt (928.9) during unlocking, then declines through preorganization and gating to a minimum at 16 nt (578.8) (Fig. 6A; all adjacent transitions P < .005, bootstrap N = 1000). This decline reflects not loss of allosteric function but progressive channeling of diffuse coupling into focused, directed pathways. At 18 nt, coupling partially rebounds (610.1; P = .004 versus 16 nt), consistent with the proposed frustrated checkpoint in which directed pathways weaken and coupling re-emerges as nonproductive sampling (Supplementary Fig. S2A).
Figure 6.

Dynamical network analysis of allosteric communication across R-loop maturation. (A) Mean allosteric coupling intensity across all 1368 protein residues for each R-loop state, with error bars representing 95% bootstrap confidence intervals (N = 1000 resamples drawn from all 1368 residues). (B) Optimal path impedance (−ln|Cij|) for four source-sink groups across the seven states: the established REC3 α37-to-HNH route, the HNH hinge pathway, and two novel sensor pathways originating from Y450 and K1200. Lower impedance indicates more efficient allosteric communication. (C) Evolution of weighted betweenness centrality for six key hub residues, revealing a progressive migration of allosteric bottlenecks from Y450 at the TS interface (8 nt) through the L1/L2 linkers and HNH hinge (16–18 nt). Primary hubs (Y450, K692, R789, residue 768, and residue 916; thick lines) exhibit state-dependent peaks; secondary hubs (thin lines) provide contextual reference. (D) Community membership of key residue groups across R-loop states, determined by weighted Girvan–Newman edge-betweenness decomposition using GCCM-derived impedance weights and selection of the maximum-modularity partition. Cell colors indicate community identity; labels denote community number. The convergence of L1 linker, L2 linker, REC-HNH hinge, H840, and HNH-RuvC residues into community C4 at 18 nt marks a consolidated HNH-linker module at the proposed checkpoint.
We computed optimal path impedance for twelve source-sink pairs across four functional groups (Fig. 6B). Groups 1 and 2 replicate established routes from the REC3 α37 helix and HNH hinge to the catalytic core [19, 20] and serve as internal validation. Groups 3 and 4 probe pathways from Y450 and K1200, residues not previously implicated in long-range allostery, to the HNH (H840) and RuvC-I (D10) centers. All four follow a qualitatively identical trajectory: Impedance is minimal at 8 nt, rises to peak at 16 nt, then partially recovers at 18 nt, mirroring the global coupling trajectory and confirming pathway-specific rather than averaging effects. Notably, the K1200 pathway shows lower impedance than the canonical REC3 α37 route across all states (Fig. 6B), identifying the PI domain as an underappreciated long-range conduit to the active sites.
Betweenness centrality reveals a spatiotemporally ordered migration of allosteric bottlenecks (Fig. 6C). Y450 shows a sharp, transient centrality spike at 8-nt (0.088), precisely coinciding with the sgRNA unstacking that permits extension beyond the seed [15]. Because Y450 maintains constitutive sgRNA contact across all states yet achieves high centrality only here, it functions as a primed sensor: Permanently anchored at the junction but activated as a signaling node exclusively during the seed-to-extension transition. At later states, the L1 linker (768), L2 linker (916), and HNH hinge R789 show concurrent centrality increases, tracing propagation of the allosteric signal toward the catalytic center. Community structure analysis (modularity Q = 0.79–0.82) shows that network fragmentation peaks at 16 nt and consolidates at 18 nt into a single dominant community, yet this integration does not confer competence: The concurrent rebound in coupling and impedance indicates the re-emerging connectivity lacks the directional fidelity of the earlier productive pathways (Supplementary Fig. S2; Supplementary Note 5). Independently, backbone flexibility, secondary structure integrity, and GCCM coupling colocate synchronous extrema at 16-nt and a consistent rebound at 18-nt, providing convergent support for the checkpoint (Supplementary Fig. S12). To identify the most state-sensitive residues, we ranked all 1 368 by cross-state variance of coupling intensity (k = 54) and peak betweenness centrality (k = 89), providing the MD-derived inputs for integration with complementary deep-learning analyses (Supplementary Fig. S13; Supplementary Tables S5 and S6).
Cross-modal triangulation establishes high-confidence allosteric residue nominations
To evaluate MD-derived nominations with analyses based on different inputs, we applied two deep-learning approaches. The VESM, implemented with an ESM2-3B backbone and VESM distilled weights, uses masked-marginal LLRs to estimate model-inferred substitution intolerance from protein sequence patterns [45]; it is not a direct measurement of evolutionary conservation. CB scoring uses ProteinMPNN to quantify structure-conditioned sequence compatibility across the seven R-loop backbones [46, 47], yielding a state-directional conformational-selectivity score rather than a physical energy. CB and VESM are uncorrelated across positions (Spearman ρ = −0.038 across 1368 positions), supporting their use as complementary (but not error-free or fully independent) evidence streams alongside MD.
Median-split quadrant analysis of CB driving force against VESM substitution intolerance (Fig. 7A) stratifies the MD-annotated residues, drawn from five independently defined categories (structural switch, GCCM variance, salt bridge and hydrophobic partner switching, and betweenness centrality), into four classes. Higher − meanLLR indicates that alternative amino acids are less compatible with sequence patterns learned by VESM; it should not be read as direct sequence conservation. Q1 core drivers (high CB, high substitution intolerance; 13 superhubs, including Y450, R925, R63, V922, M495) combine strong conformational bias with low predicted tolerance and therefore suit loss-of-function rather than fidelity-tuning experiments. Q2 functional invariants (low CB, high substitution intolerance; 15 superhubs) are predicted to be substitution-intolerant but conformationally neutral. Q4 plastic drivers (high CB, low substitution intolerance; 11 superhubs, including Q771, K961, Y1242, A538, V1018, R1210, F1037, K772, A1034, Y271, L625) combine state-selective structural compatibility with higher model-predicted sequence tolerance, making them appropriate candidates for fidelity engineering. A percentile-based consensus across all three metrics identifies 83 residues exceeding the 50th percentile in each, spanning the BH, REC1-B, RuvC-I, and RuvC-III regions (Supplementary Fig. S14; Supplementary Note 1).
Figure 7.

CB driving force versus VESM substitution intolerance for all 1368 SpCas9 residues. (A) Scatter plot of mean stepwise CB driving force (−ZCB,bias, averaged across six R-loop transitions) against position-level VESM substitution intolerance (−meanLLR). Higher − meanLLR indicates that alternative amino acids are less compatible with sequence patterns learned by VESM; it is not a direct measure of sequence conservation. Dashed lines indicate the respective medians, dividing residues into Q1 core drivers, Q2 functional invariants, Q4 plastic drivers, and Q3 background. Dot color indicates MD evidence: gray, no MD category; blue, one category; red with border, superhub supported by at least two categories. The five MD categories annotate 311 unique residues, of which 52 pass the stringent superhub filter. Superhubs are labeled; Spearman correlation is shown. (B) Quadrant composition showing total residue count (light fill), MD-annotated subset (solid fill), and superhub subset (hatched) per quadrant.
The partition generates a falsifiable prediction: Q4 residues should be more substitution-tolerant than Q1. Cross-referencing the deep mutational scanning (DMS) of SpCas9 by Spencer and Zhang [48] supports it: tolerance differs significantly across quadrants (Kruskal–Wallis P = 1.7 × 10−12), with Q4 more tolerant than Q1 (Mann–Whitney P = 1.3 × 10−10) and Q2. DMS tolerance is uncorrelated with CB but negatively correlated with position-level VESM substitution intolerance, as expected. Adding CB to a VESM-based fitness classifier does not improve AUROC because CB was designed to report conformation selectivity, not substitution fitness; the null result therefore does not by itself prove statistical independence. The DMS data validate the substitution-intolerance axis and the predicted Q4 enrichment, while CB contributes a distinct, state-directional structural criterion (Supplementary Figs S15 and S16; Supplementary Table S7; Supplementary Note 2).
Convergence with established high-fidelity variants further anchors the framework. Applying the unified ranking to the 351 Q4 residues without prior knowledge of engineered variants, three of the four published high-fidelity sites in Q4 (K961, V1018, K1031) fall within the top 14 (hypergeometric P = 6.1 × 10−4), recovering the SuperFi [51] PAM-distal cluster and the Slaymaker hit K961 [22] from first principles (Table 1). Conversely, Y1010 localizes to Q1 with a DMS median log2FC of −2.12, correctly predicting the activity loss of SuperFi Y1010D. Beyond recovered variants, three Q4 superhubs with no prior characterization emerge as triple-convergent candidates: Y271 in REC2 (DMS log2FC = +2.81), R1210 in PI (+0.52), and L625 in REC3 (+0.02), each combining MD superhub status, high CB selectivity, and confirmed mutational tolerance (Table 1). CB directionality analysis further shows that a substantial fraction of the circuit operates bidirectionally, with 138 residues reversing conformational bias during progression (Supplementary Fig. S17; Supplementary Note 2).
Table 1.
Top 20 Q4 (plastic driver) residues ranked by the unified hub-first framework. Residues are sorted by Hub_Overlap_Count (descending), then CB driving force (descending). CB force = mean(−ZCB,bias) across six stepwise R-loop pairs; VESM substitution intolerance = −meanLLR from VESM masked-marginal scores (higher values indicate lower model-predicted tolerance, not direct conservation); DMS = median log2FC from the positive-selection assay. TC, triple-convergent candidate
| Rank | Position | WT | Domain | Hub | CB force | VESM | DMS log2FC | Published variant | TC |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 771 | Q | L1 | 2 | 0.633 | 0.886 | −0.496 | ||
| 2 | 961 | K | RuvC-III | 2 | 0.400 | 1.896 | −0.003 | Slaymaker K961A | |
| 3 | 1242 | Y | PI | 2 | 0.360 | 0.668 | −0.390 | ||
| 4 | 538 | A | REC3 | 2 | 0.315 | 1.018 | −0.333 | Sniper F539S neighbor | |
| 5 | 1018 | V | RuvC-III | 2 | 0.310 | 1.233 | −0.583 | SuperFi V1018D | |
| 6 | 1210 | R | PI | 2 | 0.295 | 0.598 | +0.520 | Yes | |
| 7 | 1037 | F | RuvC-III | 2 | 0.287 | 0.160 | −0.752 | ||
| 8 | 772 | K | L1 | 2 | 0.225 | 2.608 | −0.480 | ||
| 9 | 1034 | A | RuvC-III | 2 | 0.155 | 1.005 | −0.475 | ||
| 10 | 271 | Y | REC2 | 2 | 0.058 | 2.919 | +2.807 | Yes | |
| 11 | 625 | L | REC3 | 2 | 0.058 | 1.966 | +0.020 | Yes | |
| 12 | 1029 | I | RuvC-III | 1 | 1.138 | 0.102 | −0.553 | ||
| 13 | 251 | N | REC2 | 1 | 0.870 | 2.185 | −0.059 | ||
| 14 | 1031 | K | RuvC-III | 1 | 0.817 | 1.771 | +0.024 | SuperFi K1031D | |
| 15 | 947 | D | RuvC-III | 1 | 0.667 | 2.673 | +0.642 | ||
| 16 | 64 | L | BH | 1 | 0.635 | 2.733 | +0.784 | ||
| 17 | 201 | I | REC2 | 1 | 0.561 | 1.576 | −0.546 | ||
| 18 | 586 | R | REC3 | 1 | 0.522 | 0.345 | N/A | ||
| 19 | 182 | D | REC2 | 1 | 0.487 | 0.796 | N/A | ||
| 20 | 186 | I | REC2 | 1 | 0.478 | -0.384 | −0.095 |
Residues are sorted by Hub_Overlap_Count (descending), then CB driving force (descending). CB force = mean(−ZCB,bias) across six stepwise R-loop pairs; VESM substitution intolerance = −meanLLR from VESM masked-marginal scores (higher values indicate lower model-predicted tolerance, not direct conservation); DMS = median log2FC from the positive-selection assay. TC, triple-convergent candidate. Rows 1–11 are MD superhubs (Hub_Overlap_Count ≥ 2); rows 12–20 are single-category hubs, sorted by CB force. CB force, structure-conditioned conformational-bias driving force; VESM, Variant Effect Score Model masked-marginal substitution-intolerance score; DMS, deep mutational scanning; TC, triple-convergent (Q4 superhub with DMS log2FC > 0). Bold rows denote triple-convergent engineering candidates (R1210, Y271, L625). Published variant kinds: strict = exact published substitution; screen = tested in alanine scan; adjacent = neighboring position. Bold entries identify the three triple-convergent candidate residues (R1210, Y271, and L625), which meet the criteria for MD super-hub status, high conformational-bias driving force, and positive median DMS log2 fold change. Bold formatting does not indicate statistical significance.
Experimental testing of computational nominations
The framework nominated three triple-convergent residues, Y271, R1210, and L625, across the REC2, PI, and REC3 regions, as candidates for activity-modulating substitution. We tested these with seventeen additional constructs using a GFxFP single-strand-annealing reporter in HEK293T cells, in which Cas9 cleavage restores fluorescence and the GFP-positive fraction reports cleavage activity at the engineered locus (Fig. 8; Supplementary Table S8). Each construct was assayed in triplicate at 24, 48, and 72 h, with the GFP-positive population resolved into GFP-low and GFP-high subpopulations.
Figure 8.

Experimental testing of nominated substitutions in a GFxFP cleavage reporter.(A) Total GFP-positive fraction at 72 h for each construct, ranked, with the wild-type value indicated by the dashed line. Bars show the mean of three replicates; error bars show the standard error of the mean. Coloured markers above each bar denote the predicted class: plastic driver, core driver, or control and benchmark. (B) Fraction of GFP-positive cells reaching the GFP-high state at 72 h, reflecting the rate and completeness of editing. R1210D and eSpCas9(1.1) occupy a low-completion group separated from the remaining constructs. (C) The three substitutions at R1210, showing that charge reversal but not charge neutralization reproduces the eSpCas9 phenotype; the value above each bar is the GFP-high fraction. (D) Total GFP-positive fraction at 24, 48, and 72 h for selected constructs. All values are means of three replicates.
At R1210, the three substitutions produced a graded response tracking the chemistry of the introduced residue. R1210A and R1210Q retained or slightly exceeded wild-type activity (28.8% and 27.9% total GFP-positive at 72 h versus 24.7% for wild type), whereas R1210D reduced it to 13.9% and lowered the GFP-high fraction to 1.0% from 7.4% (Fig. 8A and C; Supplementary Table S8). The high-fidelity enzyme eSpCas9(1.1) [22], assayed in parallel, showed a comparable reduction in total activity, consistent with the lower cleavage rate that accompanies its specificity. The fraction of GFP-positive cells reaching the GFP-high state, which reflects the rate and completeness of editing rather than discrimination, was 0.07 for R1210D and 0.08 for eSpCas9(1.1), separating both from all other constructs (0.29–0.39) (Fig. 8B). Because charge reversal, not charge neutralization, produced this phenotype, the effect is consistent with an electrostatic contribution of R1210 to nontarget-strand engagement. R1210D therefore occupies the same attenuated, low-completion phenotype as a validated high-fidelity enzyme, identifying it as a candidate for direct fidelity testing rather than establishing improved fidelity on its own.
At L625, alanine and aspartate substitutions both retained near-wild-type activity (25.6% and 24.1% at 72 h; GFP-high ratios 0.35 and 0.33; Fig. 8A and B; Supplementary Table S8), consistent with its assignment as a plastic-driver residue whose conformational coupling does not depend on a specific side chain.
Several substitutions increased cleavage activity above wild type. The largest increases occurred at Q771 and K772, adjacent residues in the L1 linker (33.6% and 32.7% at 72 h; Fig. 8A; Supplementary Table S8). Substitutions at the REC2 residue Y271 produced comparable increases across all three chemistries tested (18.6% to 29.4% above wild type), agreeing with the gain-of-function direction recorded for this position in the DMS data. The L1 linker and REC2 both concentrate structural switch residues and rearrange during late precatalytic gating. Because L1 ordering couples R-loop completion to HNH docking, the increased endpoint signal after Q771/K772 substitution is consistent with relief of this late gating restraint and a lower barrier to HNH repositioning. The reporter assay does not resolve which microscopic kinetic step changes, so this assignment remains a mechanistic hypothesis.
Not all predictions were concordant. The two core-driver residues tested, M495 and R925, were predicted to reduce activity but instead increased it (12.8% and 19.0% above wild type; Fig. 8A; Supplementary Table S8). For M495, this matches the M495V substitution in evoCas9 [52], where it raises activity, indicating a restraint that the core-driver classification did not capture. R925 has no comparable precedent and is identified here as a position where the activity prediction was not borne out. The reporter measures cleavage at a single locus and does not resolve off-target engagement or processivity, under which evolutionarily constrained positions may be selected, so concordance for core-driver residues may depend on the phenotype assayed.
The screen identifies R1210 as an engineerable position whose charge-reversal substitution reproduces the kinetic signature of a high-fidelity enzyme, confirms the substitution tolerance predicted for L625, and identifies the L1 linker as a negative regulator of cleavage. The full time course for all constructs is provided in Supplementary Fig. S18 (representative constructs in Fig. 8D). Because the GFxFP assay quantifies cleavage at a single matched target, it cannot distinguish reduced activity from improved discrimination, and a direct test of whether R1210D confers fidelity will require parallel on-target and off-target measurement at genomic loci, which we identify as the priority next step.
Discussion
Our analysis reveals that SpCas9 R-loop maturation is not a continuous transition but a discrete, three-stage mechanical program, unlocking (6-to-10-nt), preorganization (10-to-14-nt), and precatalytic gating (14-to-18-nt), culminating in a proposed dynamically frustrated 18-nt checkpoint. Whereas cryo-EM captures the 18-nt intermediate as a static structure [15], our dynamic analysis recasts it as a state in which HNH and REC2 recover mobility from the quenched 16-nt intermediate without committing to cleavage-competent rotation, while the allosteric bridge community fragments and reorganizes. This is consistent with smFRET observations that HNH adopts a stable docked intermediate upon full R-loop formation, with the subsequent transition to the competent state being rate limiting [13]. The gear-and-wedge model of Lu et al. [14], derived from complementary MD simulations and Markov state analyses, similarly implicates L1/L2 remodeling, REC2 displacement, and transient REC2-HNH contacts in HNH activation; our state-resolved network analysis extends this picture by locating these motions within an R-loop-length-associated allosteric program.
The checkpoint may contribute to discrimination fidelity, but the present data do not directly establish that role. Off-target complexes with PAM-distal mismatches support partial R-loop extension but fail to cleave efficiently, potentially reflecting an inability to generate sufficient strain to resolve the checkpoint. Within the two-step kinetic model of Shi et al. [5], the proposed frustrated state could represent the second, conformationally gated barrier controlling catalytic commitment. We therefore propose a testable conformational-proofreading model in which delayed irreversible commitment increases the opportunity for a mismatched complex to dissociate before cleavage. Direct matched-versus-mismatched structural, kinetic, or ensemble characterization is required to test this interpretation. HypaCas9 [53] provides precedent for such a mechanism: smFRET shows that it stabilizes HNH in an inactive conformation on mismatched targets, and Li et al. [21] showed that diverse perturbations converge on HNH immobilization through distinct upstream pathways, suggesting that HNH gating can act as an integrative hub.
Our analysis also expands the conventional view of the Cas9 allosteric landscape by highlighting RuvC-III. While prior models cast the REC lobe and HNH as the principal effectors [19, 20], the enrichment of structural switches within RuvC-III (49% of the total) argues for an active signaling role: Rather than a rigid scaffold, RuvC-III functions as an allosteric node whose coordinated Folder/Melter transitions accommodate R-loop strain and coordinate NTS contacts, redistributing order within the domain rather than rigidifying uniformly (Supplementary Fig. S6). This is reinforced by orthogonal AI validation, as key RuvC-III switches including I1029 and K1031 map to the Q4 plastic-driver quadrant. Upstream, the L1 linker’s bifurcated Folder/Melter architecture preserves connectivity along the REC-HNH-RuvC corridor, rationalizing the overrepresentation of L1 mutations in engineered high-fidelity variants.
Two candidate sensor residues define the residue-level architecture. Y450 maintains constitutive sgRNA contact across all seven states yet shows a sharp transient betweenness peak exclusively at the 8-nt unlocking stage, providing a network-level rationale for the Y450A phenotype. K1200, although established as a PAM-interacting residue [3, 4], has not been identified as an allosteric relay; our analysis reveals a long-range conduit from the PI domain to the HNH center with impedance consistently lower than the canonical REC3 α37 route [19, 20]. Cas9 therefore monitors maturation through two parallel channels: Hybrid extension sensed by the REC lobe, and NTS sliding displacement sensed by the PI domain via K1200. This dual-sensor architecture rationalizes why PI-domain perturbations affect fidelity beyond what PAM recognition alone predicts.
These findings translate into engineering guidance. The Q4 retrospective recovers three of four published high-fidelity sites [22, 51] within the top 14 of 351 residues, and the DMS cross-reference externally validates the CB × VESM stratification. Beyond recovered variants, the three triple-convergent candidates Y271, R1210, and L625 emerge as the highest-priority novel nominations, each combining MD superhub status, high CB selectivity, and confirmed mutational tolerance. Among the Q1 core drivers, R63 and V922 remain untested targets for loss-of-function experiments that test pathway necessity, while the Y450A phenotype independently supports the Q1 designation.
Experimental testing supported selected predictions while refining their interpretation. The clearest outcome, R1210, lies in the PI domain adjacent to the K1200 sensor, directly connecting the reporter result to the structural feature highlighted by the framework. R1210D reproduces the attenuated, low-completion reporter phenotype of eSpCas9(1.1) [22], and the requirement for charge reversal rather than neutralization suggests an electrostatic role in nontarget-strand engagement. Because a single matched-target reporter cannot separate reduced activity from improved discrimination, this phenotype identifies R1210D as a fidelity candidate rather than establishing improved fidelity; parallel on-target and off-target measurements are required. The largest activity increases occurred at Q771 and K772 in L1 and at Y271 in REC2. Their locations and MD behavior support a hypothesis that these substitutions perturb the late precatalytic gating step, including L1 ordering and HNH docking, although the endpoint reporter cannot identify the affected microscopic rate constant.
Two predictions were not concordant. M495 and R925, both Q1 core drivers predicted to lose activity, instead increased it. For M495 the direction matches M495V in evoCas9 [52], which increases activity, so the framework identified the position correctly but assigned the wrong direction; this is itself informative, since M495 is one of four substitutions in the yeast-selected evoCas9, and the on-target gain we observe is consistent with a restraint whose disruption could enhance discrimination on mismatched targets, a test that remains to be done. For R925 no precedent exists. These cases indicate that high VESM substitution intolerance at a core-driver position can reflect selection on properties a single-locus reporter does not measure, marking the boundary of what the present validation establishes.
Three methodological constraints warrant acknowledgment. First, HNH coordinates for the 12-nt state were grafted from the 14-nt conformation; all replicas equilibrated within 100 ns (Supplementary Fig. S1), and the three-stage framework and 18-nt checkpoint are defined by transitions outside the 12-nt state. Second, the seven starting structures were trapped using different PAM-distal mismatch substrates whose identity covaries with nominal R-loop length. Consequently, the simulations cannot causally attribute every interstate difference to R-loop extension alone, and the 16–18-nt changes may include substrate-specific contributions. We therefore treat the structures as independent trapped ensembles and the stage model as a hypothesis that requires validation using matched-sequence intermediates or controlled mismatch series. Third, the cellular reporter uses one matched target and cannot assess specificity. Disruption of transient REC2-HNH contacts formed during the 16–18-nt transition and mutations within the RuvC-III 1022–1050 segment remain testable routes for modulating the proposed checkpoint in direct matched-versus-mismatched assays.
The transferability of this workflow depends on structural coverage. When only one or two experimental structures are available, endpoint ensemble MD and state-specific allosteric paths can still generate hypotheses, but the number, order, and direction of intermediate stages are less secure. Enhanced sampling, restrained intermediate modeling, Markov-state analysis, and orthogonal kinetic or structural data are then needed to test path continuity. Predicted intermediates, including AlphaFold3 models [23], can be useful hypothesis-generating inputs but are not equivalent to experimentally trapped states: Confidence metrics, physical restraints, independent replicas, and sensitivity to alternative starting models should be reported, and the possibility that predictors favor stable endpoints rather than kinetically populated intermediates should be considered. In the present work, AlphaFold3 was used only to complete small unresolved regions of experimentally determined structures, not to generate the seven R-loop states de novo.
Taken together, these findings support a distributed, dynamic model for conformational gating in SpCas9. The three-stage trajectory, proposed 18-nt frustrated checkpoint, RuvC-III/L1 signaling corridor, and dual Y450/K1200 sensor architecture define an integrated circuit that may contribute to catalytic commitment. The model emerges from complementary evidence streams, ensemble dynamics from MD, sequence-based substitution intolerance and structure-conditioned conformational selectivity from deep-learning models, and mutational tolerance from DMS, and selected residue nominations were tested in a reporter assay. A nominated PI-domain substitution reproduced the attenuated reporter signature of a high-fidelity enzyme [22], and L1 substitutions identified this linker as a negative regulator of endpoint cleavage. These observations provide experimentally supported engineering hypotheses, not proof of improved discrimination. Direct matched-target and mismatched-target cleavage measurements for R1210D and mechanistic testing of the predicted intermediates are the immediate next steps.
Supplementary Material
Acknowledgements
The authors acknowledge the Beijing Super Cloud Center (BSCC) for providing HPC resources that have contributed to the research results reported within this paper (http://www.blsc.cn/).
Author contributions: Jianxiang Huang (Conceptualization [lead], Data curation [lead], Formal analysis [lead], Investigation [lead], Methodology [lead], Validation [lead], Visualization [lead], Writing – original draft [lead]), Jiacheng Wei (Data curation [supporting], Formal Analysis [supporting], Investigation [supporting], Methodology [supporting], Validation [supporting], Visualization [supporting], Writing – original draft [supporting]), Huazhang Chen (Data curation [supporting], Formal Analysis [supporting], Investigation [supporting], Methodology [supporting]), Xin Qiao (Data curation [supporting], Formal Analysis [supporting], Validation [supporting], Visualization [supporting]), Ning Liu (Conceptualization [supporting], Resources [supporting], Supervision [supporting]), Shaoyong Lu (Conceptualization [lead], Funding acquisition [lead], Project administration [lead], Supervision [lead], Writing – review & editing [lead]).
Contributor Information
Jianxiang Huang, Artificial Intelligence Clinical Research Center for Drug Discovery, Shanghai Key Laboratory of Flexible Medical Robotics, Institute of Medical Robotics, Tongren Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200336, China; Key Laboratory of Protection, Development and Utilization of Medicinal Resources in Liupanshan Area, Ministry of Education, Peptide & Protein Drug Research Center, School of Pharmacy, Ningxia Medical University, Yinchuan 750004, China; Department of Pharmaceutical and Artificial-Intelligence Sciences, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China.
Jiacheng Wei, Artificial Intelligence Clinical Research Center for Drug Discovery, Shanghai Key Laboratory of Flexible Medical Robotics, Institute of Medical Robotics, Tongren Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200336, China; Department of Pharmaceutical and Artificial-Intelligence Sciences, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China.
Huazhang Chen, Department of Pharmaceutical and Artificial-Intelligence Sciences, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China.
Xin Qiao, Department of Pharmaceutical and Artificial-Intelligence Sciences, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China.
Ning Liu, Key Laboratory of Protection, Development and Utilization of Medicinal Resources in Liupanshan Area, Ministry of Education, Peptide & Protein Drug Research Center, School of Pharmacy, Ningxia Medical University, Yinchuan 750004, China.
Shaoyong Lu, Artificial Intelligence Clinical Research Center for Drug Discovery, Shanghai Key Laboratory of Flexible Medical Robotics, Institute of Medical Robotics, Tongren Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200336, China; Key Laboratory of Protection, Development and Utilization of Medicinal Resources in Liupanshan Area, Ministry of Education, Peptide & Protein Drug Research Center, School of Pharmacy, Ningxia Medical University, Yinchuan 750004, China; Department of Pharmaceutical and Artificial-Intelligence Sciences, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China.
Supplementary data
Supplementary data is available at NAR online.
Conflict of interest
None declared.
Funding
This work was supported by the Noncommunicable Chronic Diseases–National Science and Technology Major Project of China (grant number 2024ZD0531200), Ministry of Science and Technology of the People's Republic of China, and by the Program for Innovative Research Team of High-Level Local Universities in Shanghai, Shanghai Municipal Education Commission. The open access publication charge for this article was funded by the Noncommunicable Chronic Diseases–National Science and Technology Major Project of China (grant number 2024ZD0531200).
Data availability
The raw data, residue-level tables, AI-derived model scores, molecular dynamics trajectories, and associated analysis data supporting the findings of this study are deposited in Zenodo (DOI: 10.5281/zenodo.22689874), the version of record used in this paper, and maintained on the GitHub repository https://github.com/HuangJianxiang-SJTU/Dynamically_frustrated_checkpoint. Raw flow cytometry data from the GFP reporter assays in HEK293T cells are provided in the Source Data file. Source data are provided with this paper. Initial structures for the molecular dynamics simulations were obtained from the RCSB PDB database. Molecular dynamics simulations were performed with the AMBER suite, available at https://ambermd.org/. The deep mutational scanning data used for cross-validation were taken from Spencer and Zhang [48]. AI-based fitness evaluation used VESM (https://github.com/ntranoslab/vesm) and Conformational Biasing (https://github.com/alicetinglab/ConformationalBiasing). Analysis code is archived in Zenodo (DOI: 10.5281/zenodo.22689874) and maintained on GitHub (https://github.com/HuangJianxiang-SJTU/Dynamically_frustrated_checkpoint).
References
- 1. Jinek M, Chylinski K, Fonfara I et al. A programmable dual-RNA–guided DNA endonuclease in adaptive bacterial immunity. Science. 2012;337:816–21. 10.1126/science.1225829 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2. Jiang F, Doudna JA. CRISPR–Cas9 structures and mechanisms. Annu Rev Biophys. 2017;46:505–29. 10.1146/annurev-biophys-062215-010822 [DOI] [PubMed] [Google Scholar]
- 3. Nishimasu H, Ran FA, Hsu PD et al. Crystal structure of Cas9 in complex with guide RNA and target DNA. Cell. 2014;156:935–49. 10.1016/j.cell.2014.02.001 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4. Anders C, Niewoehner O, Duerst A et al. Structural basis of PAM-dependent target DNA recognition by the Cas9 endonuclease. Nature. 2014;513:569–73. 10.1038/nature13579 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5. Shi H, Al-Sayyad N, Wasko KM et al. Rapid two-step target capture ensures efficient CRISPR–Cas9-guided genome editing. Mol Cell. 2025;85:1730–42.e9. 10.1016/j.molcel.2025.03.024 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6. Eggers AR, Chen K, Soczek KM et al. Rapid DNA unwinding accelerates genome editing by engineered CRISPR–Cas9. Cell. 2024;187:3249–61.e14. 10.1016/j.cell.2024.04.031 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 7. Sternberg SH, LaFrance B, Kaplan M et al. Conformational control of DNA target cleavage by CRISPR–Cas9. Nature. 2015;527:110–3. 10.1038/nature15544 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8. Szczelkun MD, Tikhomirova MS, Sinkunas T et al. Direct observation of R-loop formation by single RNA-guided Cas9 and Cascade effector complexes. Proc. Natl. Acad. Sci. USA. 2014;111:9798–803. 10.1073/pnas.1402597111 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9. Hsu PD, Scott DA, Weinstein JA et al. DNA targeting specificity of RNA-guided Cas9 nucleases. Nat Biotechnol. 2013;31:827–32. 10.1038/nbt.2647 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10. Fu Y, Foden JA, Khayter C et al. High-frequency off-target mutagenesis induced by CRISPR–Cas nucleases in human cells. Nat Biotechnol. 2013;31:822–6. 10.1038/nbt.2623 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11. Jiang F, Taylor DW, Chen JS et al. Structures of a CRISPR–Cas9 R-loop complex primed for DNA cleavage. Science. 2016;351:867–71. 10.1126/science.aad8282 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12. Huai C, Li G, Yao R et al. Structural insights into DNA cleavage activation of CRISPR–Cas9 system. Nat Commun. 2017;8:1375. 10.1038/s41467-017-01496-2 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 13. Dagdas YS, Chen JS, Sternberg SH et al. A conformational checkpoint between DNA binding and cleavage by CRISPR–Cas9. Sci Adv. 2017;3:eaao0027. 10.1126/sciadv.aao0027 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 14. Lu S, Li X, Wei J et al. Untangling the molecular mechanism of SpCas9 catalytic activation: a gear-and-wedge fitting model. Res. Sq., 10.21203/rs.3.rs-6018412/v1, 4 March 2025, preprint: not peer reviewed. [DOI]
- 15. Pacesa M, Loeff L, Querques I et al. R-loop formation and conformational activation mechanisms of Cas9. Nature. 2022;609:191–6. 10.1038/s41586-022-05114-0 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16. Palermo G, Miao Y, Walker RC et al. Striking plasticity of CRISPR–Cas9 and key role of non-target DNA, as revealed by molecular simulations. ACS Cent Sci. 2016;2:756–63. 10.1021/acscentsci.6b00218 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 17. Palermo G, Ricci CG, Fernando A et al. Protospacer adjacent motif-induced allostery activates CRISPR–Cas9. J Am Chem Soc. 2017;139:16028–31. 10.1021/jacs.7b05313 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 18. Ricci CG, Chen JS, Miao Y et al. Deciphering off-target effects in CRISPR–Cas9 through accelerated molecular dynamics. ACS Cent Sci. 2019;5:651–62. 10.1021/acscentsci.9b00020 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19. East KW, Newton JC, Morzan UN et al. Allosteric motions of the CRISPR–Cas9 HNH nuclease probed by NMR and molecular dynamics. J Am Chem Soc. 2020;142:1348–58. 10.1021/jacs.9b10521 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 20. Nierzwicki Ł, Arantes PR, Saha A et al. Establishing the allosteric mechanism in CRISPR–Cas9. WIREs Comput Mol Sci. 2021;11:e1503. 10.1002/wcms.1503 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21. Li Y, Li X, Chen Y et al. Differential allosteric modulation of Cas9 specificity. J Chem Theory Comput. 2026;22:806–17. 10.1021/acs.jctc.5c01919 [DOI] [PubMed] [Google Scholar]
- 22. Slaymaker IM, Gao L, Zetsche B et al. Rationally engineered Cas9 nucleases with improved specificity. Science. 2016;351:84–8. 10.1126/science.aad5227 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 23. Abramson J, Adler J, Dunger J et al. Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature. 2024;630:493–500. 10.1038/s41586-024-07487-w [DOI] [PMC free article] [PubMed] [Google Scholar]
- 24. DeLano WL. PyMOL: an open-source molecular graphics tool. CCP4 Newsletter on Protein Crystallography. 2002;40:82–92. [Google Scholar]
- 25. Case DA, Cerutti DS, Cruzeiro VWD et al. Recent developments in amber biomolecular simulations. J Chem Inf Model. 2025;65:7835–43. 10.1021/acs.jcim.5c01063 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 26. Tian C, Kasavajhala K, Belfon KAA et al. ff19SB: amino-acid-specific protein backbone parameters trained against quantum mechanics energy surfaces in solution. J Chem Theory Comput. 2020;16:528–52. 10.1021/acs.jctc.9b00591 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27. Zgarbová M, Otyepka M, Šponer J et al. Refinement of the Cornell et al. Nucleic acids force field based on reference quantum chemical calculations of glycosidic torsion profiles. J Chem Theory Comput. 2011;7:2886–902. 10.1021/ct200162x [DOI] [PMC free article] [PubMed] [Google Scholar]
- 28. Ivani I, Dans PD, Noy A et al. Parmbsc1: a refined force field for DNA simulations. Nat Methods. 2016;13:55–8. 10.1038/nmeth.3658 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 29. Jorgensen WL, Chandrasekhar J, Madura JD et al. Comparison of simple potential functions for simulating liquid water. J Chem Phys. 1983;79:926–35. 10.1063/1.445869 [DOI] [Google Scholar]
- 30. Joung IS, Cheatham TE III. Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations. J. Phys. Chem. B. 2008;112:9020–41. 10.1021/jp8001614 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 31. Humphrey W, Dalke A, Schulten K. VMD: visual molecular dynamics. J Mol Graphics. 1996;14:33–8. 10.1016/0263-7855(96)00018-5 [DOI] [PubMed] [Google Scholar]
- 32. Palermo G, Chen JS, Ricci CG et al. Key role of the REC lobe during CRISPR–Cas9 activation by ‘sensing’, ‘regulating’, and ‘locking’ the catalytic HNH domain. Quart Rev Biophys. 2018;51:e91. 10.1017/S0033583518000070 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33. Abraham MJ, Murtola T, Schulz R et al. GROMACS: high performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX. 2015;1-2:19–25. 10.1016/j.softx.2015.06.001 [DOI] [Google Scholar]
- 34. Kabsch W, Sander C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers. 1983;22:2577–637. 10.1002/bip.360221211 [DOI] [PubMed] [Google Scholar]
- 35. Naughton FB, Alibay I, Barnoud J et al. MDAnalysis 2.0 and beyond: fast and interoperable, community driven simulation analysis. Biophys J. 2022;121:272a–3a. 10.1016/j.bpj.2021.11.1368 [DOI] [Google Scholar]
- 36. Michaud-Agrawal N, Denning EJ, Woolf TB et al. MDAnalysis: a toolkit for the analysis of molecular dynamics simulations. J Comput Chem. 2011;32:2319–27. 10.1002/jcc.21787 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 37. Lange OF, Grubmüller H. Generalized correlation for biomolecular dynamics. Proteins. 2006;62:1053–61. 10.1002/prot.20784 [DOI] [PubMed] [Google Scholar]
- 38. Sethi A, Eargle J, Black AA et al. Dynamical networks in tRNA:protein complexes. Proc. Natl. Acad. Sci. USA. 2009;106:6620–5. 10.1073/pnas.0810961106 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 39. Girvan M, Newman MEJ. Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA. 2002;99:7821–6. 10.1073/pnas.122653799 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40. Wei J, Chen F, Lu X et al. In silico identification and experimental validation of long-range allosteric inhibition of Staphylococcus aureus Cas9 catalytic activity by an anti-CRISPR protein AcrIIA14. Int J Biol Macromol. 2025;310:143324. 10.1016/j.ijbiomac.2025.143324 [DOI] [PubMed] [Google Scholar]
- 41. Blondel VD, Guillaume J-L, Lambiotte R et al. Fast unfolding of communities in large networks. J Stat Mech. 2008;2008, P10008. 10.1088/1742-5468/2008/10/P10008 [DOI] [Google Scholar]
- 42. del Sol A, Fujihashi H, Amoros D et al. Residues crucial for maintaining short paths in network communication mediate signaling in proteins. Mol Syst Biol. 2006;2:MSB4100063. 10.1038/msb4100063 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 43. Yen JY. Finding the K shortest loopless paths in a network. Management Science. 1971;17:712–6. 10.1287/mnsc.17.11.712 [DOI] [Google Scholar]
- 44. Hagberg AA, Schult DA, Swart PJ. Exploring network structure, dynamics, and fuction using NetworkX. In Proceedings of the 7th Python in Science Conference, (pp.11–5.). Pasadena, CA: SciPy, 2008. 10.25080/TCWV9851 [DOI] [Google Scholar]
- 45. Dinh T, Jang SK, Zaitlen N et al. Compressing the collective knowledge of ESM into a single protein language model. Nat Methods. 2026;23:772–84. 10.1038/s41592-026-03050-9 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 46. Dauparas J, Anishchenko I, Bennett N et al. Robust deep learning–based protein sequence design using ProteinMPNN. Science. 2022;378:49–56. 10.1126/science.add2187 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 47. Cavanagh PE, Xue AG, Dai SA et al. Computational design of conformation-biasing mutations to alter protein functions. Science. 2026;391:eadv7953. 10.1126/science.adv7953 [DOI] [PubMed] [Google Scholar]
- 48. Spencer JM, Zhang X. Deep mutational scanning of S. pyogenes Cas9 reveals important functional domains. Sci Rep. 2017;7:16836. 10.1038/s41598-017-17081-y [DOI] [PMC free article] [PubMed] [Google Scholar]
- 49. Cofsky JC, Soczek KM, Knott GJ et al. CRISPR–Cas9 bends and twists DNA to read its sequence. Nat Struct Mol Biol. 2022;29:395–402. 10.1038/s41594-022-00756-0 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 50. Ferreiro DU, Hegler JA, Komives EA et al. On the role of frustration in the energy landscapes of allosteric proteins. Proc. Natl. Acad. Sci. USA. 2011;108:3499–503. 10.1073/pnas.1018980108 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 51. Bravo JPK, Liu M-S, Hibshman GN et al. Structural basis for mismatch surveillance by CRISPR–Cas9. Nature. 2022;603:343–7. 10.1038/s41586-022-04470-1 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 52. Casini A, Olivieri M, Petris G et al. A highly specific SpCas9 variant is identified by in vivo screening in yeast. Nat Biotechnol. 2018;36:265–71. 10.1038/nbt.4066 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 53. Chen JS, Dagdas YS, Kleinstiver BP et al. Enhanced proofreading governs CRISPR–Cas9 targeting accuracy. Nature. 2017;550:407–10. 10.1038/nature24268 [DOI] [PMC free article] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The raw data, residue-level tables, AI-derived model scores, molecular dynamics trajectories, and associated analysis data supporting the findings of this study are deposited in Zenodo (DOI: 10.5281/zenodo.22689874), the version of record used in this paper, and maintained on the GitHub repository https://github.com/HuangJianxiang-SJTU/Dynamically_frustrated_checkpoint. Raw flow cytometry data from the GFP reporter assays in HEK293T cells are provided in the Source Data file. Source data are provided with this paper. Initial structures for the molecular dynamics simulations were obtained from the RCSB PDB database. Molecular dynamics simulations were performed with the AMBER suite, available at https://ambermd.org/. The deep mutational scanning data used for cross-validation were taken from Spencer and Zhang [48]. AI-based fitness evaluation used VESM (https://github.com/ntranoslab/vesm) and Conformational Biasing (https://github.com/alicetinglab/ConformationalBiasing). Analysis code is archived in Zenodo (DOI: 10.5281/zenodo.22689874) and maintained on GitHub (https://github.com/HuangJianxiang-SJTU/Dynamically_frustrated_checkpoint).
