Representation choice shapes the interpretation of protein conformational dynamics

Axel Giottonini; Thomas Lemmin

cs.LGApr 1, 2026

Representation choice shapes the interpretation of protein conformational dynamics

Authors: Axel Giottonini, Thomas Lemmin

Organizations: Institute of Biochemistry and Molecular Medicine, University of Bern, Bühlstrasse 28, Bern, 3012, Bern, Switzerland . · Graduate School for Cellular and Biomedical Sciences (GCB), University of Bern, Mittelstrasse 43, Bern, 3012, Bern, Switzerland . · Department of Digital Medicine, University of Bern, Murtenstrasse 31, Bern, 3008, Bern, Switzerland .

Abstract

Molecular dynamics simulations provide detailed trajectories at the atomic level, but extracting interpretable and robust insights from these high-dimensional data remains challenging. In practice, analyses typically rely on a single representation. Here, we show that representation choice is not neutral: it fundamentally shapes the conformational organization, similarity relationships, and apparent transitions inferred from identical simulation data. To complement existing representations, we introduce Orientation features, a geometrically grounded, rotation-aware encoding of protein backbone. We compare it against common descriptions across three dynamical regimes: fast-folding proteins, large-scale domain motions, and protein-protein association. Across these systems, we find that different representations emphasize complementary aspects of conformational space, and that no single representation provides a complete picture of the underlying dynamics. To facilitate systematic comparison, we developed ManiProt, a library for efficient computation and analysis of multiple protein representations. Our results motivate a comparative, representation-aware framework for the interpretation of molecular dynamics simulations.

Figures & tables

Figure 1: Orientation Features Workflow. ( 1 ) A Local Coordinate System is constructed for each residue from the amide nitrogen (N), alpha carbon (C $\alpha$ ), and carbonyl carbon (C) positions, forming an orthonormal basis. ( 2 ) Each LCS is aligned to the per-residue intrinsic mean orientation and projected onto the tangent space at the identity element of SO(3), yielding features in the Lie algebra $\mathfrak{so}(3)$ .

Figure 2: Kinetic Characterization of Fast-Folding Proteins. ( A ) VAMP-2 scores for each molecular representation (y-axis) evaluated at the comparison lag time. Systems are shown along the x-axis. ( B , left ) TICA landscapes of 1FME for Orientation $\odot$ and torsion angle representations. The x- and y-axes show TIC1 and TIC2, respectively, with implied timescales annotated. Points are colored by Orientation $\odot$ cluster assignment; darker shades indicate unassigned frames. ( B , right ) Representative centroid structures for each cluster, shown in cartoon representation.

Figure 3: nsp13 Gram Matrices Analysis. ( A ) Gram matrices for Orientation and Orientation $\odot$ representations. Axes represent time across merged trajectories; color intensity indicates pairwise inner product values. Black squares highlight closed-like conformations. Top row: full Gram matrices. Bottom row: first two rank-1 projection matrices. ( B ) Spearman correlation coefficients between Gram matrices and structural similarity measures. Blue bars: correlation with RMSD; red bars: correlation with lDDT. Inner bars show correlations for rank-1 components.

Figure 4: nsp13 Clusters. ( A ) Clustering agreement across representations. Upper triangle: Adjusted Rand Score; lower triangle: Adjusted Mutual Information. ( B ) PC1–PC2 projections for each representation. Points are colored by Orientation $\odot$ cluster assignment. ( C ) Centroid structures of the five most populated Orientation $\odot$ clusters in panel B, aligned on the stalk and RecA1 domains. The monomeric nsp13 protein is shown in a ribbon representation, with domains color-coded as follows: ZB (orange), Stalk (pink), 1B (yellow), RecA1 (red) and RecA2 (Purple).

Figure 5: Molecular Representations for Barnase–Barstar Association. Results for ( A ) Orientation $\odot$ , ( B ) C $\alpha$ coordinates, and ( C ) torsion angles. In all panels: ( .1 ) PC1 (y-axis) versus IRMSD (x-axis). Interacting frames shown in purple-to-orange gradient (by IRMSD); non-interacting frames in orange. Gray region: interquartile range $[Q_{1}{-}1.5\,\mathrm{IQR},\,Q_{3}{+}1.5\,\mathrm{IQR}]$ ; Pearson Correlation Coefficient (PCC) annotated. In all panels: ( .2 ) PC1 density distributions for interacting/non-interacting states with quartile lines. In all panels: ( .3 ) Reference structure (Barstar: light gray; Barnase: dark gray). Top 10 PC1-contributing residues highlighted in red; hydrogen bonds shown as dashed lines (red: involving contributors; blue: other).

Figure 6: Landscape of RBD-ACE2 Association. ( A ) PC1–PC2 projection of the Orientation $\odot$ (u) representation. Points colored by cluster assignment. ( B ) Time series of the distance between protein centers of geometry. The x-axis represents time; y-axis shows distance. Colors indicate cluster assignment. ( C ) Centroid structures of the four bound-state clusters. Upper region: ACE2 receptor; lower region: RBD. The receptor-binding motif (RBM) is highlighted in blue.

Figure 7: ManiProt Profile. ( A, B ) Computational scaling of the SO(3) ( A ) and Pointcloud ( B ) logarithmic maps. The x-axis shows the number of residues; y-axis shows the number of frames. Color indicates the log-ratio of execution time relative to the smallest problem size (1 (SO(3)) and 2 (Pointcloud) residue, 1 frame). ( C ) Scaling of Pointcloud-associated operations (metric tensor (Met. ten.) computation and inversion (inv.)). The x-axis shows the number of residues; y-axis shows the log-ratio of execution time relative to 4 residues.

Figure S1: WW Domain Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S2: $\lambda$ -Repressor Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S3: Protein G Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S4: Villin Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S5: Trp-Cage Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S6: BBL Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S7: BBA Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S8: $\alpha$ 3D Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S9: Protein B Analysis. ( Row 1 ) Implied timescales vs. lag time (log scale); dark/light blue: TIC1/TIC2. ( Row 2 ) TIC1–TIC2 projections colored by Orientation $\odot$ clusters (gray: outliers). ( Row 3 ) TIC1 ( left ) and TIC2 ( right ) time series by cluster. ( Row 4 ) DSSP heatmap (blue: $\alpha$ -helix; red: $\beta$ -sheet) ( left ); column-normalized metrics heatmap (EVR1/2, t1/2, VAMP-2) ( right ).

Figure S10: BBA Clusters. ( Top ) DCCM heatmaps (red: correlation; blue: anti-correlation). ( Middle ) DCOM heatmaps (red/blue: $\pm 180\deg$ between residue normal vectors). ( Bottom ) Cluster medoid structures. Colors match Supplementary Figure S7 .

Figure S11: $\alpha$ 3D Clusters. ( Top ) DCCM heatmaps (red: correlation; blue: anti-correlation). ( Middle ) DCOM heatmaps (red/blue: $\pm 180\deg$ between residue normal vectors). ( Bottom ) Cluster medoid structures. Colors match Supplementary Figure S8 .

Figure S12: Protein B Clusters. ( Top ) DCCM heatmaps (red: correlation; blue: anti-correlation). ( Middle ) DCOM heatmaps (red/blue: $\pm 180\deg$ between residue normal vectors). ( Bottom ) Cluster medoid structures. Colors match Supplementary Figure S9 .

Figure S13: nsp13 Gram Matrices. ( Top ) Gram matrices for each representation across merged trajectories. ( Bottom ) First two rank-1 components from eigendecomposition.

Figure S14: nsp13 Gram Matrices - RMSD Correlation. Scatterplots of Gram matrix scores vs. RMSD. ( Top ) Full Gram matrices. ( Bottom ) Rank-1 components.

Figure S15: nsp13 Gram Matrices - lDDT Correlation. Scatterplots of Gram matrix scores vs. lDDT. ( Top ) Full Gram matrices. ( Bottom ) Rank-1 components.

Figure S16: nsp13 Clusters. PC1–PC2 projections for each representation, colored by cluster assignment. Rows correspond to different clustering assignments.

Figure S17: nsp13 Clusters Structures. Orientation $\odot$ cluster centroids aligned on stalk and RecA1 domains. Colors match Supplementary Figure S16 .

Figure S18: Protein-Protein Association Mutual Information. MI between association state and PC1–PC2 ( left ) or PC1 alone ( right ) for each representation. Colors indicate systems.

Figure S19: Barnase-Barstar PC1 Distribution. ( Top ) PC1 time series for each representation. ( Bottom ) Violin plots of PC1 by association state (B: bound; U: unbound); lines indicate quartiles.

Figure S20: Insulin Dimer (0) PC1 Distribution. ( Top ) PC1 time series for each representation. ( Bottom ) Violin plots of PC1 by association state (B: bound; U: unbound); lines indicate quartiles.

Figure S21: Insulin Dimer (1) PC1 Distribution. ( Top ) PC1 time series for each representation. ( Bottom ) Violin plots of PC1 by association state (B: bound; B’: non-canonical bound; U: unbound); lines indicate quartiles.

Figure S22: RNaseHI-SSB Complex PC1 Distribution. ( Top ) PC1 time series for each representation. ( Bottom ) Violin plots of PC1 by association state (B: bound; U: unbound); lines indicate quartiles.

Figure S23: RBD-ACE2 Clusters. PC1–PC2 projections for each representation, colored by cluster assignment. Rows correspond to different clustering solutions.

System	N. Frames (total)	N. Frames (analyzed)	Stride	Time ( $\mu s$ )
BBA	1’625’195	1’625’195	1	325.0
Villin	627’907	627’907	1	125.0
Trp-cage	1’044’000	1’044’000	1	208.0
BBL	2’150’146	2’150’146	1	429.0
$\alpha$ 3D	3’535’447	3’535’447	1	707.0
WW domain	5’686’712	5’686’712	1	1’137.0

Table S1: Simulation Details. Number of frames –total and analyzed–, subsampling stride and time in

\mu

s of the systems analyzed.

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