Principal component analysis of (𝛔2-𝛔4) - SnoaL2 correlated motions
We also carried out the Principal Component Analysis (PCA), i.e., essential dynamics of the covariance matrix resulting from the 200ns MD trajectories, to investigate the underlying interactions at the NPDKV and DGGGR motifs and their impact on the overall domain motions. Principal components (PC) analysis was applied to the backbone atoms of the RpoE10 and RpoE10 (Mut1, Mut2, and Del1) forms. PC analysis is used to reveal the functionally relevant and most dominant internal modes of motion of a MD simulation 35,36. We chose PC1, the most crucial component, accounting for maximum variability in protein conformation and computed eigenvectors and associated eigenvalues (variance). Covariance values provide information about the correlated motion. All diagonal elements of the covariance matrix were summed and termed as trace values, which provide information about the measure of the total variance. As shown in the scatter plot of PC1 vs. PC2 (Figure. 7A-D), the RpoE10 (Del1) and RpoE10 (Mut1) occupy larger subspaces corresponding to their higher trace values of the covariance matrix 63.03 (nm2) and 58.51 (nm2), respectively, as compared to RpoE10 (37.16 nm2) and RpoE10(Mut-2) (43.58 nm2) (Figure. 7(A-D) ). The higher trace values of RpoE(Del1) and RpoE10(Mut1) relative to the wild-type RpoE10 and RpoE10(Mut2) suggested an association with an enhanced flexible behavior upon mutation in NPDKV or the deletion of the proximal SnoaL2 domain. We observed that the cumulative variance captured by the first 20 eigenvectors of RpoE10 (wild type) is lower as compared to the RpoE10(Mut1) and RpoE10(Del1) (Figure 7E). The RpoE10 (Mut1) and RpoE (Del1) showed 72% and 80% variance, respectively, of the cumulative proportion of the total variance captured by the first five eigenvectors (Supplemental Table S4). This suggests that the mutation at the NPDKV motif has impacted the RpoE10-SnoaL2 correlated motions. The first two principal components PC1 and PC2 account for ~55% and ~64% of the total variance of all the motions for RpoE10 (Mut1) and RpoE10(Del1), respectively, as compared to ~ 49% in RpoE10 and  50% in RpoE10(Mut2) ( Supplemental Table S4). The high eigenvalues, i.e., the variance of the covariance matrix in both RpoE10 (Mut1) and RpoE10 (Del1), indicate the signals for critical transitions in the conformational changes lead to enhanced activation. Percentages of variance against eigenvalues of the covariance matrix resulting from simulations are shown in Figure 7E.
Furthermore, we correlated the elimination or activation of the promoter with the global protein motion in RpoE10 and RpoE10 (Mut1 and Mut2) and RpoE10 (Del1) using PCA analysis (Figure 7F, G, H, and I). The mutation at NPDKV and DGGGR greatly influences the SnoaL_2 domain and overall dynamics of 2-𝝈4 domain, and magnifies the significant conformational movements (Figure 7H and I). The PCA indicated that the essential motion of RpoE10(Mut1) and RpoE10(Del1) was dominated by fluctuations of the critical L3 loop (residues 46-52), also termed as “flexibility loop” and Arginine Tetrad (residues 73-76) (marked by a dotted circle and double arrow and an in Figure 7F, G, H and I) of the 𝛔2 domain. Another noticeable and differential key fluctuation was observed in the orientation of helix-α7 of 𝛔4 domain (marked by a dotted square in Figure 7 F, G, H, and I). The helix-α7 constitutes a helix-turn-helix motif that recognizes the -35 element of the promoter 34 (Figure 4A). The principal differential movements of the backbone atoms at -10 and -35 recognition and residues involved in promoter recognition was further recorded from the average structures of RpoE10 and its variant obtained from the PC1 (Figure S2).
A close inspection at -10 promoter binding cleft revealed correlated motions in RpoE10(Mut1) and RpoE10 (Del1); however, RpoE10 and RpoE10 (Mut2) forms exhibited a significant anti-correlated motion (Figure 7 (bottom panel) and Figure S2A and B). More minor fluctuations in RpoE10, as well as RpoE10(Mut2) in comparison to RpoE10 (Mut1) and RpoE10(Del1) were observed in the specificity loop, L3- connecting α2 and α3 (marked with a circle in Figure 7 (F,G,H, and I)). This differential flexibility of the L3-loop and orientation of the helix may directly affect the binding to the promoter region and thus impact the promoter activity. Notably, the wide-open cleft of -10 recognition site with reduced flexibility of L3-loop (shown by the blue double arrow in Figure 7) in both RpoE10 and RpoE10 (Mut2) may constrain the 𝛔2-𝛔4 domain in an “open” and unproductive conformation leading to the elimination of promoter activity (Figure 7 ). Another contrasting movement both in the direction and distance was observed at the WLPEP motif of RpoE10 (Mut1) and RpoE10(Del1) as compared to RpoE10 and RpoE10(Mut2) (Figure 7, bottom panel). We noticed an increase in the distance between the initial and final conformation of Cα for W83 and P87 in RpoE10 (Mut1) and RpoE10 (Del1) as compared to RpoE10 and RpoE10(Mut2) (Figure 7 (bottom panel) and Supplemental Table S5.) Intriguingly, we find that WLPEP motif moves inward-up in both RpoE10 and RpoE10(Mut2), whereas in RpoE10(Mut1) and RpoE10(Del1), the movements are outward-up and outward-down, respectively. This differential inward and outward trajectories of the WLPEP motif suggest that it may act as a sensor in transmitting the conformational signal from the Snoal_2 domain to2-𝛔4domains.