A new approach for extracting information from protein dynamics

Abstract

Increased ability to predict protein structures is moving research focus towards understanding protein dynamics. A promising approach is to represent protein dynamics through networks and take advantage of well-developed methods from network science. Most studies build protein dynamics networks from correlation measures, an approach that only works under very specific conditions, instead of the more robust inverse approach. Thus, we apply the inverse approach to the dynamics of protein dihedral angles, a system of internal coordinates, to avoid structural alignment. Using the well-characterized adhesion protein, FimH, we show that our method identifies networks that are physically interpretable, robust, and relevant to the allosteric pathway sites. We further use our approach to detect dynamical differences, despite structural similarity, for Siglec-8 in the immune system, and the SARS-CoV-2 spike protein. Our study demonstrates that using the inverse approach to extract a network from protein dynamics yields important biophysical insights.

Figure 1.. Unraveling structural properties from protein conformational dynamics.

(A) Cartoon illustrating the three adhesion proteins studied here. FimH refers to the lectin domain of a bacterial adhesin found in uropathogenic E. coli that binds mannose and undergoes a conformational change under tensile force from urine flow. Siglec-8 refers to the lectin domain of a human immune-inhibitory protein found on eosinophils and mast cells. The SARS-CoV-2 RBD and SD1 domains are thought to undergo a down-to-up transition that makes the RBD available to bind ACE2. For each protein, we compare pairs states: FimH_L wild type (PDB 4AUU) and mutant (PDB 5MCA), Siglec-8 with ligand 6’S-sLe^x (PDB 2N7B) and without (PDB 2N7A), and RBD-SD1 in down and up (PDB 6VSB) states. (B) Comparison of covariance analysis of the dynamics (top left) versus the inverse covariance analysis (bottom right) from the dynamics of wild type FimH_L (see Figure S1, S2, and S3 for the other proteins). While many studies rely on the analysis of the covariance matrix, our data clearly shows that the structure of the covariance matrix is dominated by artifacts (vertical and horizontal lines) which are stronger for side chain interactions (red square for χ₁ − χ₁). In contrast, the inverse covariance matrix clearly reveals a structure reminiscent of a contact map and is dominated by backbone interactions (blue square for ψ − ψ).

Figure 2.. Inverse covariance matrix is robust across replicates whereas covariance and correlation matrices are not.

(A) Triangular regions above and below the matrix diagonal show results from two replicates of wild type FimH_L starting from the same protein structure. We show ψ − ψ interactions. We show interaction strength in blue with a normalization for each triangular region made based on the 97^th percentile of observed strengths. In red, we show the ratio for interaction strength between the two replicates. Purple indicates strong interactions that are not reproduced in the other replicates. (See Figure S5 for weaker interactions visible when normalized to the 95^th percentile for ψ − ψ and χ₁ − χ₁.) For covariance and correlation matrices, we find that backbone-backbone interactions are mostly quite weak, but the strong interactions (darker blue) vary drastically between replicates. In contrast, for the inverse covariance matrix, the strongest backbone-backbone are symmetric across the diagonal. (B) To evaluate the robustness of network inference, we calculate the Jaccard similarity coefficient for the covariance, correlation, and inverse covariance analyses methods across three simulation replicates. We define edges above the threshold of ≥97^th percentile. (See Figure S7 for other thresholds.) In grey scale, we show similarity separately for ψ − ψ and χ₁ − χ₁ interactions. Darker grey indicates results are similar across replicates for the inverse covariance approach and much less similar for the other two methods. (C) The inverse covariance matrix resembles the contact map. We show the Cα inter-residue distance from the crystal structure. Darker grey indicates shorter distance.

Figure 3.. The inverse covariance matrix enables us to extract a “contact map”-like network from the protein dynamics.

(A) Comparison of strong interactions identified for the covariance matrix (top left) and for the inverse covariance matrix (bottom right) of wild type FimH. To provide context for our data, we plot the 12 Å contact map in grey within the matrix. On the top and right axes we show helix (pink) and strand (teal) secondary structures assigned by the Dictionary of Secondary Structure of Proteins algorithm (DSSP). On the left and bottom axes we show putative allosteric pathway landmarks: pocket zipper (red), clamp segment (yellow), swing loop (cyan), β-bulge (purple), α-switch (green), insertion loop (blue), and linker loop (dark red). We only show strong edges, with the threshold set at the 97^th percentile of all dihedral interactions. See Figure S6 for other cutoffs. We averaged edge weight across three replicates. The blue dots represent the average of backbone-backbone interactions by residue. The red crosses represent sidechain-sidechain interactions (χ₁ − χ₁). The inverse covariance network are predominantly backbone interactions that fall within the 12 Å contact map. There is a ≥ 99^th percentile χ₁ − χ₁ interaction the Cys3-Cys44 disulfide bond (red arrow). However, this interaction is only 80^th percentile in strength (green diamond and arrow) for the covariance matrix, which is dominated by other χ₁ − χ₁ interactions. (B) Since the covariance matrix has many long-range interactions, we only show the backbone interactions and the sidechain interactions for Lys4. In contrast, the inverse covariance network has mostly short-range interactions, including the disulfide bond. We show backbone interactions on the Cα atoms and sidechain interactions on the the 4^th χ₁ atoms. We show backbone interactions in blue and sidechain interactions in red. Darker colors indicate stronger interactions.

Figure 4.. Inverse covariance analysis can detect both large and small structural changes in FimH_L.

(A) Comparing inferred networks for wild type and mutant proteins, we show differences in the backbone (top left in dots) and χ₁ − χ₁ (bottom right in crosses). As in Figure 3A, we annotate the 12 Å distance cutoff, secondary structures, and landmarks. The black dots on the colorbar mark the 97^th percentile in magnitude. On the adjacency matrix, we show all differences greater than 2σ. (B) On the protein, we show large differences (≥ 97^th %ile). Red shows interactions stronger for mutant fimH_L; blue for WT fimH_L. We highlight the pocket zipper (red), insertion loop (blue), and β-bulge/α-switch (green) and (C) show isolated parts of the network. (D) Comparing wild type FimH with the Cys3-Cys44 disulfide bond intact or reduced in silico. (E) The blue lines shows that the Cys3-Cys44 χ₁ − χ₁ (blue arrow) and the Phe43-Cys44 backbone-backbone interactions are stronger when the disulfide bond is intact.

Figure 5.. Inferred networks identify strong interactions and changes in interaction strength.

(A) Illustration of Siglec-8 highlighting the CC’ loop of the binding pocket in orange, Arg70 in cyan, and hypothesized hydrogen bond acceptor carbonyl oxygens (black spheres) for ensemble of 20 NMR structures. From MD simulations of all structures, we show snapshots every 10ns for the (B) Cys31-Cs91 disulfide bond, (C) Arg79-Asp102 salt bridge, and (D) CC’ loop. Structures were aligned to the backbone atoms for residues 13–135 to exclude the N- and C-terminus tails. These snapshots show the stability of the salt bridge and disulfide bond, and the surprising stability of the unstructured CC’ loop. However, the hypothesized interaction between Arg70 and the CC’ loop is much less stable, even with (E) structural alignment using the backbone of the CC’ loop. (F) Beyond identifying strong interactions, our approach also identifies rearrangements of strong interactions without large structural changes in Siglec-8 and the SARS-CoV-2 RBD-SD1. Siglec-8 with (holo) and without (apo) ligand have similar structures. However, inverse covariance analysis reveals rearrangement of strong interactions in a region opposite the binding pocket, including the Cys31-Cys91 disulfide bond (black spheres). We show interactions stronger in holo (red) and apo (blue) on the holo structure. (G) For the SARS-CoV-2 spike protein, rotation around the RBD-SD1 hinge exposes the RBD in the up conformation (Figure 1A), while the structures with the RBD hidden are extremely similar (down1, down2, and off conformation). Comparing inferred network interactions, we detect differences near the hinge, including the Cys336-Cys361 disulfide bond (black spheres) and nearby α-helices. For these regions, we show the interactions that are stronger in the down2 (blue) and off (red) conformations on the corresponding structure. See Figure S15 for other comparisons.