Chemical Shift Guided Structure Generation

• Chemical shift guided structure generation is a method that uses NMR observables to constrain candidate 3D structures for biomolecules and small molecules.
• It integrates simulation, Bayesian energy scoring, and machine learning to maximize agreement between predicted and observed NMR data.
• Recent advances include inverse design via diffusion models and genetic algorithms, enhancing automated structure elucidation across diverse molecular systems.

Chemical shift guided structure generation leverages experimental or predicted nuclear magnetic resonance (NMR) chemical shifts to constrain, rank, or directly generate candidate molecular structures, both for biomacromolecules and small molecules/crystals. By integrating chemical shift observables with simulation, machine learning, or generative modeling frameworks, this approach seeks to maximize agreement between predicted and observed NMR data, thereby enhancing accuracy and confidence in 3D structure elucidation across molecular domains.

1. Theoretical Basis: Chemical Shifts as Structural Observables

Chemical shifts are sensitive probes of local electronic structure; they depend on local geometry, hydrogen bonding, and the broader electronic environment. In proteins, amide proton chemical shifts correlate with backbone dihedral angles, H-bond geometries, and proximal aromatic rings, while in small molecules, shifts of ^1H, ^13C, ^15N, and ^17O capture both constitution and conformation. The backbone amide proton shift model, as realized in ProCS and Padawan, exemplifies this structural sensitivity, decomposing δ_pred into backbone (φ,ψ), primary and cooperative H-bond, and ring current terms, all parameterized against high-level quantum chemical (QM) reference data (Christensen, 2015, Christensen et al., 2013). For molecular solids and organic compounds, Gaussian Process Regression (GPR) models using local atomic environments predict chemical shifts at density functional theory (DFT) accuracy, enabling rapid evaluation across combinatorial chemical spaces (Paruzzo et al., 2018). Limitations remain: while chemical shifts constrain local conformational space effectively, their information content for global topology or stereochemistry is limited without augmentation by additional NMR observables.

2. Energy Scoring and Bayesian Integration

The translation of chemical shift agreement into a statistical or energetic framework underpins chemical shift guided structure generation. Bayesian likelihoods treat shift agreement as a pseudo-energy in protein modeling, e.g.,

$$E_\text{shift}(X) = \sum_{i=1}^N \frac{[\delta_\text{obs,i} - \delta_\text{pred,i}(X)]^2}{2\sigma_i^2} + \sum_{i=1}^N \ln(\sigma_i \sqrt{2\pi}),$$

where σ_i encodes estimated prediction error by shift class (Christensen, 2015, Christensen et al., 2013). This term is incorporated on equal footing with physical force fields (e.g., OPLS, PROFASI) in hybrid energy functions for Markov Chain Monte Carlo (MCMC) sampling or refinement (Larsen, 2014). For crystal structure elucidation, both Bayesian posterior probabilities and simple RMSD metrics over shifts serve to rank candidate structures, with uncertainty estimation critical for robust confidence assignment (Engel et al., 2019).

3. Methodologies: From Refinement to Direct Inverse Design

Protein Modeling

Quantum parameterized, rapidly evaluated predictors such as ProCS and Padawan are embedded within the PHAISTOS framework. Candidate protein structures generated by MC or diffusion generative models are scored not only by physical potential but by their predicted chemical shift agreement. Movesets include local φ/ψ/χ backbone and side-chain updates, while chemical shift energy is recalculated only for residues whose geometry is altered (Christensen et al., 2013, Christensen, 2015, Larsen, 2014). Chemshift extends this approach via fully Bayesian chemical shift assignment, handling assignment uncertainty, weighting, and integration into the folding/refinement engine (Bratholm, 2013).

A recent advance is non-differentiable guidance of generative models via genetic algorithms (GA), where black-box shift prediction tools (e.g., UCBShift) form the fitness landscape for evolutionary optimization over the latent space of a diffusion model. This decouples the need for model differentiability and enables conditional generation of protein backbones or sidechains to maximize shift agreement (Sellam et al., 17 Nov 2025).

Small Molecule and Crystallography

In small-molecule NMR crystallography, the workflow is:

1. Candidate structure enumeration (e.g., by CSP, graph enumeration)
2. Structure relaxation (e.g., DFT-level geometry optimization)
3. Chemical shift prediction (DFT or ML, e.g., ShiftML)
4. Calculation of a matching score (RMSD, likelihood, or Bayesian posterior)
5. Ranking and selection/acceptance thresholding (e.g., H RMSE <0.49 ppm) (Paruzzo et al., 2018, Engel et al., 2019)

Machine learning driven methods such as ShiftML use local environment SOAP descriptors and GPR for fast prediction with calibrated uncertainties (Paruzzo et al., 2018). Bayesian posteriors incorporating uncertainties enable both robust ranking and automated alerts when the "true" structure is unlikely to be represented in the candidate pool (Engel et al., 2019).

Inverse Design and Fully Generative Models

For direct structure generation conditioned on chemical shifts, the approach generalizes to:

• Diffusion models (e.g., DiSE) ingesting chemical shifts as node features, with the conditional generation of molecular graphs aimed at reconstructing the observed spectra (Chen et al., 30 Oct 2025).
• Spectra matching as an inverse design problem, wherein an algorithm searches a database of candidate structures, evaluates predicted shifts, and selects those with minimal RMSD to the observed data. Numerical analysis shows error tolerance is doubled when using both ^1H and ^13C spectra, and performance is highly dependent on chemical space constraint (Lemm et al., 2023).

4. Algorithms, Implementation, and Performance

Protein Chemical Shift Scoring Models

Predictor	Backbone Model	H-Bond Term	Ring Current	Typical σ (amide-H)	PHAISTOS Integration
ProCS	0.828·[ICS(φ,ψ)+0.77 ppm]	Barfield (r, θ, ρ)	Point-dipole	0.3–1.2 ppm	Bayesian E_shift in MC
Padawan	Czinki–Császár 10th-order	Barfield (analytic/formamid)	Pople	0.3–1.2 ppm	E_shift, no global weight
Procs14	QM tripeptide hypersurfaces	Explicit 1°, 2° H-bond	Point-dipole	user-specified	ISD-style likelihood

Procs14 enables rapid MC evaluation through optimized grid lookup, local caching, and parallelization (Larsen, 2014).

Small Molecule/NMR Crystallography

Method	Descriptor	Shift Model	Error (H, C)	Workflow Component
ShiftML	SOAP (multi)	GPR	0.49, 4.3 ppm	Crystal structure ranking/assignment
Bayesian+ShiftML	SOAP	GPR/PP/ensemble	0.48, 4.13 ppm	Posterior probability calculation

Efficient strategies include reduction of candidate pool via stoichiometry, functional group, or reaction context, and incorporating uncertainty estimation for both DFT and ML shift predictions (Lemm et al., 2023, Engel et al., 2019).

Generative Conditional Models

Chemical shift guided generation via diffusion models (DiSE) or guided diffusion plus GA (Seek and You Shall Fold) achieves high Top-1 structure recovery (over 90% with 2D spectra) provided error in chemical shifts is within the model's tolerance. For small molecules, accurate matching is possible up to ∼10^4–10^5 isomer pools with 0.9–1.0 ppm error, but heteroatom-rich pools demand sub-ppm accuracy (Chen et al., 30 Oct 2025, Lemm et al., 2023).

5. Limitations and Sources of Ambiguity

Chemical shift data by itself typically encodes strong local but weak global structural information. For proteins, chemical shifts primarily restrict local φ/ψ and hydrogen bond networks, while global topology remains underdetermined (Christensen, 2015, Christensen et al., 2013). In small molecules, constitutional and (with 1D NMR) stereochemical ambiguities are prevalent. Augmentation with additional data modalities (e.g., 2D HSQC, COSY, NOEs, RDCs in proteins) is necessary for robust structure recovery at scale (Chen et al., 30 Oct 2025, Sellam et al., 17 Nov 2025). Existing chemical shift predictors can be non-differentiable and may underperform on exotic environments, solvent-exposed protons, or systems outside their training domains. Model limitations are mitigated by integrating uncertainty quantification, expanded training sets, and multi-modal data (Engel et al., 2019, Paruzzo et al., 2018).

6. Impact, Applications, and Future Directions

Chemical shift guided structure generation is now a pivotal component in:

• Automated protein structure refinement and validation
• NMR crystallography workflows, both with DFT and ML-predicted shifts
• Self-driving laboratory platforms for small-molecule structure elucidation
• Generative modeling frameworks, including diffusion and evolutionary algorithms

The integration of Bayesian uncertainty, assignment robustness, and efficient ML predictors enables rapid, scalable structure determination with quantitative confidence metrics (Engel et al., 2019, Paruzzo et al., 2018, Sellam et al., 17 Nov 2025).

Future directions include development of differentiable, biophysically grounded shift models for end-to-end conditional generation, explicit treatment of solvent and ensemble averaging, and deeper integration with high-throughput, multi-modal experimental data, such as 2D NMR, NOE, and IR/Raman spectra (Sellam et al., 17 Nov 2025, Chen et al., 30 Oct 2025). Robustness to noisy experimental shifts and capacity to resolve stereochemistry and heteroatom-rich systems are active areas of research. Coupling chemical shift scoring with adaptive generative sampling promises to further close the loop between experiment, prediction, and generative modeling in autonomous molecular discovery.