Sequence charge decoration organizes salt response regimes in intrinsically disordered proteins: an interpretable machine-learning

Technical Summary: Sequence Charge Decoration Organizes Salt Response Regimes in Intrinsically Disordered Proteins

Problem Statement
Intrinsically disordered proteins (IDPs) exhibit conformational ensembles that are highly sensitive to ionic strength. While the direction and magnitude of this response vary widely—ranging from polyelectrolyte contraction to polyampholyte swelling—current sequence-conditioned models (e.g., ALBATROSS, STARLING) primarily predict ensemble properties at fixed conditions or generate full ensembles without explicitly identifying the low-dimensional polymer physics descriptors that organize salt response behavior. There is a need for an interpretable, reduced map that connects specific sequence features to the direction and magnitude of salt-induced conformational changes across broad sequence space.

Methodology
The authors constructed a systematic library of 511 sequences to span controlled charge compositions and patterning architectures, supplemented by natural sequences from the IDRome database. The library includes:

• $\kappa$-variants (195 sequences): Synthetic polyampholytes with near-zero net charge and systematically varied charge-patterning parameter $\kappa$.
• NCPR series (108 sequences): Synthetic chains with fixed charge fraction but titrated net charge per residue (NCPR) to span from neutral to strong polyelectrolytes.
• IDRome-stratified (150 sequences): Natural human IDRs sampled to cover the corners of the $(SCD, N)$ space.
• IDRome low-FCR (58 sequences): Weakly charged natural sequences.

Simulations:
All sequences were simulated using the CALVADOS-2 coarse-grained model across five monovalent salt concentrations (50, 100, 150, 300, and 500 mM), yielding 2,555 single-chain simulations. The radius of gyration ($R_g$) was extracted to determine the salt-response slope, $b = dR_g/d[\text{salt}]$.

Regime Classification:
Based on the relative change in $R_g$ and the monotonicity of the $R_g$ vs. salt curve, sequences were classified into four regimes:

1. Polyelectrolyte (PE) contraction: Monotonically decreasing $R_g$.
2. Polyampholyte (PA) swelling: Monotonically increasing $R_g$.
3. Non-monotonic: Curves reversing direction within the salt range.
4. Salt-insensitive: Minimal change ($|\Delta_{rel}| < 0.03$).

Machine Learning Approach:
The study utilized eight theory-motivated sequence descriptors (including $N$, $FCR$, $NCPR$, $\kappa$, $SCD$, hydropathy, and their interactions) to predict the salt-response slope and classify regimes. Models included:

• Ridge Regression: A linear baseline.
• Gradient-Boosted Trees (XGBoost): To capture non-linearities.
• SHAP Analysis: To interpret feature importance and non-linear dependencies.
  Validation was performed using both random 5-fold cross-validation (in-distribution) and leave-one-subset-out (LOSO) cross-validation (out-of-distribution/generalization across sequence families).

Key Results

1. Dominant Coordinate: The sequence charge decoration weighted by chain length, $SCD \times N$, is the dominant coordinate organizing salt response. It accounts for $\sim40\%$ of total SHAP attribution, exceeding the next most important feature by more than a factor of two.
2. Regime Organization: The four regimes separate primarily along the $SCD$ axis.
   • PA swelling sequences occupy the negative tail ($SCD < -0.5$).
   • PE contraction sequences occupy the positive tail ($SCD > +1$).
   • Non-monotonic sequences cluster in the low-magnitude middle ($|SCD| < 1$).
   • Salt-insensitive sequences are distinguished not by $SCD$ but by low fraction of charged residues ($FCR < 0.10$), spreading across the entire $SCD$ axis.
3. Predictive Performance:
   • In-distribution: XGBoost achieved $R^2 = 0.97$ in predicting the salt-response slope, significantly outperforming ridge regression ($R^2 = 0.83$).
   • Out-of-distribution (LOSO): XGBoost retained predictive power ($R^2 = 0.60$), whereas ridge regression failed ($R^2 = -0.13$), indicating that salt response contains transferable but non-linear sequence-encoded structure.
4. Non-linear Dependence: The relationship between $SCD \times N$ and the response slope is sigmoidal. $SCD \times N$ sets the direction (sign) and magnitude (saturation) of the response, a behavior that linear models cannot capture, explaining the superior performance of tree-based models.
5. Classification Accuracy: The direction of response (contraction vs. swelling) is robustly predicted with no confusion between PE and PA classes. However, distinguishing non-monotonic from salt-insensitive sequences remains difficult using static sequence features alone, as both exhibit small slope magnitudes.

Significance and Claims
The paper establishes $SCD \times N$ as a compact, interpretable organizing coordinate for IDP salt response derived from CALVADOS-2 simulations. This work provides a polymer-physics, feature-level complement to ensemble-level generative models by identifying which specific descriptors govern the response to changing salt conditions rather than just the dimensions at a fixed condition.

The authors claim that their results:

• Empirically validate and quantify the role of charge patterning (specifically $SCD$) in governing salt response regimes across hundreds of sequences.
• Demonstrate that the sign of the salt response is robustly encoded by sequence charge features, while the magnitude requires non-linear modeling.
• Highlight the limitations of linear extrapolation across sequence families and the necessity of non-linear feature interactions for generalization.
• Note that the study is simulation-based; the predicted slopes are directional and relative rather than quantitatively calibrated to experiment, as CALVADOS-2 omits residue-specific salting-out and Hofmeister effects. The authors frame the work as a step toward an interpretable map of electrostatic response, distinct from but complementary to recent sequence-to-ensemble generative frameworks.