CrystalBoltz: End-to-End Protein Structure Determination via Experiment-Guided Diffusion for X-Ray Crystallography

Abstract: Generative models trained on public databases of protein structures, most of which have been determined by X-ray crystallography, now provide powerful priors for structure prediction. However, they are not readily conditioned on the measurements from a new crystallographic experiment, limiting their use for X-ray structure determination. In crystallography, the measured structure-factor amplitudes do not by themselves determine an electron density map or atomic structure because the associated phases are unobserved and must be inferred. Structure determination therefore remains an inverse problem in which candidate models must be both structurally plausible and consistent with measured diffraction data, often requiring substantial manual refinement by human experts. Emerging methods aim to incorporate experimental information more directly into predictive and refinement workflows. We present CrystalBoltz, a generative framework that casts crystallographic refinement as Bayesian inference over atomic structures and operates directly on structure-factor amplitudes. CrystalBoltz moves from unguided generation with a pre-trained prior over protein structures to experiment-guided posterior sampling, followed by atomic coordinate and B-factor refinement. Across multiple protein crystallography datasets, CrystalBoltz attains lower coordinate RMSD and lower R-factors than the strongest baselines considered, while reducing runtime by a factor of 33 relative to existing experimentally guided refinement.

• The paper demonstrates that integrating generative diffusion priors with experimental crystallographic guidance significantly improves protein structure accuracy.
• It introduces a two-stage process with diffusion-based posterior sampling followed by B-factor and coordinate refinement in the native crystallographic frame.
• The method achieves up to a 33.3× runtime speedup and substantial reductions in RMSD and R-factors compared to conventional approaches.

End-to-End Experiment-Guided Diffusion for Protein Structure Determination: CrystalBoltz

Introduction and Motivation

Protein structure resolution via X-ray crystallography remains constrained by the phase problem: only structure-factor amplitudes are measured, leaving associated phases to be inferred. While generative protein structure predictors such as AlphaFold2/3 and Boltz-2 provide strong priors, they do not guarantee consistency with experimental diffraction data. Conventional refinement pipelines—such as those implemented in Phenix and REFMAC5—are computationally intensive and depend on high-quality initializations that may not reflect experimentally observed conformational states. CrystalBoltz introduces a novel Bayesian inference framework that tightly integrates generative structure priors and differentiable physical likelihoods directly linked to crystallographic observables, enabling end-to-end structure determination with explicit experimental guidance at both global and local scales.

Figure 1: Algorithmic overview of CrystalBoltz, comprising experiment-guided Boltz-2 diffusion sampling (with mid-way activation of experimental gradients) and post-guidance coordinate/B-factor refinement.

Methodology

CrystalBoltz employs a two-stage approach:

1. Diffusion-Based Posterior Sampling:

Starting from a Boltz-2 generative prior conditioned on protein sequence and crystallographic parameters, CrystalBoltz conducts stochastic sampling where, after a "warm-up" period for rough fold formation, gradients from differentiable crystallographic likelihoods are applied to guide sampling toward structures consistent with observed structure-factor amplitudes. This guidance is implemented using Diffusion Posterior Sampling (DPS) principles [dps], injecting likelihood score gradients into the SDE trajectory only after initial structure plausibility is established.

The experimental likelihood leverages a hybrid between a Gaussian error model and the Rice distribution, the latter allowing principled treatment of amplitude-only experimental data and nontrivial phase uncertainty. Crucially, the forward model is rendered fully differentiable (including bulk solvent effects) via SFCalculator [sfcalculator]. Real-space predictions are rigidly aligned to the crystal frame at each guided step to ensure correct interpretation of reciprocal-space observables.

2. Post-Guidance Refinement:

The denoised structure from the last diffusion step undergoes a secondary refinement in the native crystallographic frame, where both atomic coordinates and isotropic B-factors are jointly optimized against either R-factor or correlation coefficient (CC) objectives. B-factors are initialized from Boltz-2 pLDDT scores and clamped to physically plausible ranges. This stage removes residual local inaccuracies (e.g., side-chain rotamers) and allows fine partitioning of disorder between coordinate and thermal motion, avoiding overfitting coordinates when amplitude mismatch arises from true atomic variability.

Experimental Results

CrystalBoltz demonstrates strong improvements over both classical (Phenix) and modern (Boltz-2, ROCKET) baselines across a diverse protein set (164–306 residues, $1.69$–$2.20$ Å resolution) by all relevant metrics (all-atom RMSD, $C_\alpha$ RMSD, $R_\mathrm{work}$, $R_\mathrm{free}$). Particularly on targets exhibiting substantial conformational deviation relative to the Boltz-2 prior, CrystalBoltz achieves reductions in global RMSD from $2.20$ Å to $1.32$ Å (8DWN) and from $4.54$ Å to $1.30$ Å (4NTZ), with concurrent significant reductions in R-factors. On easier targets where priors are already close, CrystalBoltz provides consistent incremental gains in $R_\mathrm{free}$ across the board. Critically, the full pipeline achieves a 33.3$2.20$0 runtime speedup over ROCKET ($2.20$111 minutes vs. 6+ hours for identical hardware and setup).

Figure 2: CrystalBoltz refines structure for PDB 4NTZ, recovering large conformational changes and significantly lowering RMSD and R-factor.

Figure 3: On PDB 8DWN, CrystalBoltz corrects large-scale deviations from the prior, unlike ROCKET or baseline diffusion.

Ablation and Mechanistic Analysis

Analyses highlight several mechanistically critical aspects:

• Bulk Solvent Modeling: Ablation of bulk solvent effects in SFCalculator yields substantial reduction in CC, confirming that accurate solvent modeling is essential for matching experimental amplitudes.

Figure 4: Solvent ablation on PDB 8DWN—the bulk-solvent term produces consistent improvements in the agreement metric.

• B-Factor Refinement: Disabling B-factor optimization marginally increases RMSD but leaves R-factors unchanged. Thus, B-factor refinement primarily allows correct attribution of amplitude discrepancies to motion/disorder rather than erroneous coordinate shifts.
• Guidance Scheduling: Premature activation of experimental gradients during diffusion leads to suboptimal local minima due to the noise-dominated landscape; optimal performance is observed when guidance is activated after backbone topology emerges but before post-guidance refinement. Only the combination of mid-way guidance and post-guidance B-factor/coordinate optimization yields optimal fit to both geometry and diffraction data.

Implications and Future Directions

CrystalBoltz provides an extensible template for directly integrating differentiable physics-based likelihoods into generative sampling, eliminating the need for iterative hand-tuned model building. Its tight linkage between generative priors and experimental observables makes it especially suitable for conformational states inaccessible to the training distribution (e.g., induced fit, allosteric transitions). Minute-scale runtimes open the possibility of real-time refinement during crystallographic data acquisition.

The methodology is readily extensible: both the inference engine (e.g., substituting newer DPS variants [zhang2024daps, ddiff2026]) and the physical forward model (e.g., adaptation for cryo-EM or multi-chain targets) can be generalized. A major limitation remains the coarse-to-fine reliance on a reference structure for rigid alignment; integration with robust, self-aligning forward models or direct end-to-end equivariant architectures is a promising direction.

From a broader AI/ML perspective, CrystalBoltz exemplifies the power and generality of combining deep diffusion priors and exact likelihoods for solving high-dimensional inverse problems where experimental data is incomplete, noisy, and subject to symmetry constraints. Its successes will likely motivate analogous frameworks in other domains requiring both learned and physics-based constraints.

Conclusion

CrystalBoltz establishes a high-performance, end-to-end framework for protein structure determination from X-ray crystallographic data by integrating sequence-conditioned diffusion priors and differentiable, native crystallographic likelihood guidance. It consistently attains lower RMSD and R-factor values than current state-of-the-art baselines and achieves this with a dramatic reduction in computational requirements. The approach represents a robust, extensible paradigm for experiment-conditioned structure inference and highlights new directions in the intersection of generative biomolecular modeling, computational structural biology, and the physics of high-dimensional Bayesian inverse problems.

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References:

• "CrystalBoltz: End-to-End Protein Structure Determination via Experiment-Guided Diffusion for X-Ray Crystallography" (2605.15564)
• Diffusion Posterior Sampling [dps]
• SFCalculator [sfcalculator]
• Boltz-2 [boltz2]
• ROCKET [fadini2025rocket]
• AlphaFold2/3 [jumper2021, alphafold3]
• Decoupled Noise Annealing [zhang2024daps]
• Dual Ascent Diffusion [ddiff2026]