Limits...
Mechanical network in titin immunoglobulin from force distribution analysis.

Stacklies W, Vega MC, Wilmanns M, Gräter F - PLoS Comput. Biol. (2009)

Bottom Line: We then compare the observed force pattern to the sparse network of coevolved residues found in this family.We find a remarkable overlap, suggesting the force distribution to reflect constraints for the evolutionary design of mechanical resistance in the IG family.The force distribution analysis provides a molecular interpretation of coevolution and opens the road to the study of the mechanism of signal propagation in proteins in general.

View Article: PubMed Central - PubMed

Affiliation: CAS-MPG Partner Institute for Computational Biology, Shanghai, People's Republic of China.

ABSTRACT
The role of mechanical force in cellular processes is increasingly revealed by single molecule experiments and simulations of force-induced transitions in proteins. How the applied force propagates within proteins determines their mechanical behavior yet remains largely unknown. We present a new method based on molecular dynamics simulations to disclose the distribution of strain in protein structures, here for the newly determined high-resolution crystal structure of I27, a titin immunoglobulin (IG) domain. We obtain a sparse, spatially connected, and highly anisotropic mechanical network. This allows us to detect load-bearing motifs composed of interstrand hydrogen bonds and hydrophobic core interactions, including parts distal to the site to which force was applied. The role of the force distribution pattern for mechanical stability is tested by in silico unfolding of I27 mutants. We then compare the observed force pattern to the sparse network of coevolved residues found in this family. We find a remarkable overlap, suggesting the force distribution to reflect constraints for the evolutionary design of mechanical resistance in the IG family. The force distribution analysis provides a molecular interpretation of coevolution and opens the road to the study of the mechanism of signal propagation in proteins in general.

Show MeSH

Related in: MedlinePlus

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.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2643529&req=5

pcbi-1000306-g004: 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.

Mentions: We compared the evolutionary network with the force distribution pattern in I27; hereto we restricted our analysis to inter side chain forces, (see Methods), as evolution mainly optimizes side chains. A distinct group of residues with highest evolutionary couplings, residues I23, V4, F73, I2, V30, and L84, were found to mainly couple among each other and to clearly separate from the bulk, as indicated by hierarchical clustering analysis on the coevolution data (Figure 4A) Remarkably, these evolutionarily strongly connected residues show a very strong response to the applied mechanical perturbation, being among those showing highest changes in force distribution values (Figure 4B). This suggests that evolutionary and force distribution analysis show an overlapping set of residues which are crucial for mechanical robustness (Figure 4C). The overall comparison of evolutionary couplings with inter-residue forces of all IG residues indicates a connection of the evolutionary with the mechanical network as well. ΔΔE and show a significant correlation, shown in Figure S3A, with a correlation coefficient of R = 0.52 (t = 5.56 and for 86 data points as calculated using student's t-test). This correlation is remarkable, regarding that the two data sets, from molecular simulations and sequence analysis, are completely independent. Furthermore, constraints acting on the evolution of proteins can be expected to be of manifold nature and thus to blur the correlation. One of these additional constraints is the optimization of the IG-IG interaction interface. Indeed, excluding the interfacial residues (see above) increases the correlation coefficient to R = 0.60 (with t = 6.62 and for 79 data points). For the same reason, the correlation is expected to weaken when including sequences into the alignment that are not necessarily designed to bear mechanical load. To test this, we constructed a second more diverse alignment denoted (Dataset S2), containing 282 sequences with high similarity to the I27 structure. Results from coupling analysis for overlap (Figure S3B), suggesting that the observed conservation pattern is robust with regard to the MSA. We observe a lower correlation for than for (0.37 vs. 0.52) corroborating our conclusion that the overlap found between evolutionary couplings and force distribution reflects an optimization for mechanical robustness of IG domains. Similarly, overlap of with overall residue conservation is low (R = 0.18), suggesting that it is the network rather than individual residues that are important for mechanical stability.


Mechanical network in titin immunoglobulin from force distribution analysis.

Stacklies W, Vega MC, Wilmanns M, Gräter F - PLoS Comput. Biol. (2009)

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.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2643529&req=5

pcbi-1000306-g004: 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.
Mentions: We compared the evolutionary network with the force distribution pattern in I27; hereto we restricted our analysis to inter side chain forces, (see Methods), as evolution mainly optimizes side chains. A distinct group of residues with highest evolutionary couplings, residues I23, V4, F73, I2, V30, and L84, were found to mainly couple among each other and to clearly separate from the bulk, as indicated by hierarchical clustering analysis on the coevolution data (Figure 4A) Remarkably, these evolutionarily strongly connected residues show a very strong response to the applied mechanical perturbation, being among those showing highest changes in force distribution values (Figure 4B). This suggests that evolutionary and force distribution analysis show an overlapping set of residues which are crucial for mechanical robustness (Figure 4C). The overall comparison of evolutionary couplings with inter-residue forces of all IG residues indicates a connection of the evolutionary with the mechanical network as well. ΔΔE and show a significant correlation, shown in Figure S3A, with a correlation coefficient of R = 0.52 (t = 5.56 and for 86 data points as calculated using student's t-test). This correlation is remarkable, regarding that the two data sets, from molecular simulations and sequence analysis, are completely independent. Furthermore, constraints acting on the evolution of proteins can be expected to be of manifold nature and thus to blur the correlation. One of these additional constraints is the optimization of the IG-IG interaction interface. Indeed, excluding the interfacial residues (see above) increases the correlation coefficient to R = 0.60 (with t = 6.62 and for 79 data points). For the same reason, the correlation is expected to weaken when including sequences into the alignment that are not necessarily designed to bear mechanical load. To test this, we constructed a second more diverse alignment denoted (Dataset S2), containing 282 sequences with high similarity to the I27 structure. Results from coupling analysis for overlap (Figure S3B), suggesting that the observed conservation pattern is robust with regard to the MSA. We observe a lower correlation for than for (0.37 vs. 0.52) corroborating our conclusion that the overlap found between evolutionary couplings and force distribution reflects an optimization for mechanical robustness of IG domains. Similarly, overlap of with overall residue conservation is low (R = 0.18), suggesting that it is the network rather than individual residues that are important for mechanical stability.

Bottom Line: We then compare the observed force pattern to the sparse network of coevolved residues found in this family.We find a remarkable overlap, suggesting the force distribution to reflect constraints for the evolutionary design of mechanical resistance in the IG family.The force distribution analysis provides a molecular interpretation of coevolution and opens the road to the study of the mechanism of signal propagation in proteins in general.

View Article: PubMed Central - PubMed

Affiliation: CAS-MPG Partner Institute for Computational Biology, Shanghai, People's Republic of China.

ABSTRACT
The role of mechanical force in cellular processes is increasingly revealed by single molecule experiments and simulations of force-induced transitions in proteins. How the applied force propagates within proteins determines their mechanical behavior yet remains largely unknown. We present a new method based on molecular dynamics simulations to disclose the distribution of strain in protein structures, here for the newly determined high-resolution crystal structure of I27, a titin immunoglobulin (IG) domain. We obtain a sparse, spatially connected, and highly anisotropic mechanical network. This allows us to detect load-bearing motifs composed of interstrand hydrogen bonds and hydrophobic core interactions, including parts distal to the site to which force was applied. The role of the force distribution pattern for mechanical stability is tested by in silico unfolding of I27 mutants. We then compare the observed force pattern to the sparse network of coevolved residues found in this family. We find a remarkable overlap, suggesting the force distribution to reflect constraints for the evolutionary design of mechanical resistance in the IG family. The force distribution analysis provides a molecular interpretation of coevolution and opens the road to the study of the mechanism of signal propagation in proteins in general.

Show MeSH
Related in: MedlinePlus