Figure 1.
Crystal structure and force propagation in I27.
(A) Crystal structure of I27 (PDB-entry 1WAA). Mechanical load during MD simulations is applied to I27 by pulling the termini with a constant force as indicated. All protein structures were plotted using PyMOL [61]. (B) Signal-to-noise ratio of atomic forces after mechanical loading and equilibration. The dimensionless normalized force signal, Δf, per atom after summing over all atom pairs is measured by the difference in atomic forces between strained and relaxed state (blue), and is compared to noise, estimated from normalized differences between two sets of equilibrium trajectories (gray). (C) The raw force signal, ΔF, with noise plotted in gray. Comparison with the normalized signal in (B) shows that the overall force distribution pattern is not affected by normalization, see Methods for details.
Figure 2.
(A) Graph representation of changes in interatomic forces, , observed upon mechanical perturbation of I27. Edges connect non-bonded atom pairs with
. The protein surface is shown in gray. A 3D animation of this figure is available as Video S1. (B) Changes in atomic forces, Δf, mapped onto the protein structure. Colors range from blue for elements outside the mechanical network with Δf = 0 to red for force bearing elements with high Δf. (C) Graph representation of
displayed as edges as in (A). I27 is shown as cartoon. Edges connecting main-chain atoms are colored blue, those connecting side chain atoms are colored red. Mechanical load at the C-terminus is mainly taken up by main-chain interactions around the A'G strand, whereas at the N-terminal side forces are primarily propagating into the protein core by side chain interactions.
Figure 3.
Coevolved interaction interface.
(A) Principal component analysis on the perturbation matrix (see Methods) separates a set of residues along the first component (gray numbers). (B) Mapping these residues on the adjacent titin domains I67 and I68 (PDB-Code 2RIK [30]) reveals that they apparently belong to a conserved IG-IG interaction interface. Interaction interface residues are marked as gray spheres. Edges connect highly coevolved residues (red spheres) with ΔΔE>0.7.
Figure 4.
Overlap of the mechanical and coevolutionary network.
(A) Heatmap of the clustered, symmetric coupling matrix containing ΔΔE values for each pair of residues, interaction interface residues were excluded. The cluster containing residues important for mechanical stability is marked in blue (augmented plot). Heatmap colors range from blue for ΔΔE = 0 to yellow for high ΔΔE values. (B) Comparison of evolutionary and mechanical couplings. Inter-side chain forces and evolutionary couplings ΔΔE are shown as barplots and sorted in descending order; interface residues were excluded. The six residues forming a highly connected cluster via evolutionary couplings, colored blue, are found to be among the highest
values. The average error in the (dimensionless)
values is <5 as estimated from equilibrium data (Figure 1B). (C) Structural overlap of the evolutionary with the mechanical network. The six clustered residues shown in blue in (B) mapped as spheres/sticks onto the 1WAA structure. Sticks are colored with
and spheres with ΔΔE. SCA identifies the six residues as highly coevolved, edges show couplings between these residues with ΔΔE>0.7. The secondary structure was colored with
to give an overview of the overall force distribution.
Figure 5.
Forces needed for transition into the intermediate state measured for a selected set of in silico mutations.
(A) values for the mutated residues sorted in descending order. The nine residues with highest
, for which decreased rupture forces are expected, are colored gray. (B) Rupture forces observed for transition into the intermediate. The majority of the nine residues with highest
shows a significant decrease in rupture forces comparing to the wild-type (WT), while residues with significantly lower
show less impact onto rupture forces upon mutation. The overall decrease comparing to the WT and to the six negative controls is statistically significant (p<0.01 and p<0.03, respectively, student's t-test on cumulative rupture force data. For individual p-values, see Table S1).
Figure 6.
Comparison of in silico rupture forces for the A'G strand with experimental data.
(A) Our simulations predict decreased stability of the A'G strand for 5 residues near the A'G strand, rendering them interesting targets for further experimental studies. The figure shows these residues mapped as sticks on the I27 structure. F21, L84 and V71 are colored blue, the experimentally validated V13 and V86 are colored red. (B) Changes in rupture force from experiment and simulation plotted against each other. The line shows a fit of the data to a linear model. Experimental data for a pulling speed of 10 nm s−1 were extracted from Figure 3, Best et al. 2003 [14].