Implementation of force distribution analysis for molecular dynamics simulations.

BACKGROUND: The way mechanical stress is distributed inside and propagated by proteins and other biopolymers largely defines their function. Yet, determining the network of interactions propagating internal strain remains a challenge for both, experiment and theory. Based on molecular dynamics simulations, we developed force distribution analysis (FDA), a method that allows visualizing strain propagation in macromolecules. RESULTS: To be immediately applicable to a wide range of systems, FDA was implemented as an extension to Gromacs, a commonly used package for molecular simulations. The FDA code comes with an easy-to-use command line interface and can directly be applied to every system built using Gromacs. We provide an additional R-package providing functions for advanced statistical analysis and presentation of the FDA data. CONCLUSIONS: Using FDA, we were able to explain the origin of mechanical robustness in immunoglobulin domains and silk fibers. By elucidating propagation of internal strain upon ligand binding, we previously also successfully revealed the functionality of a stiff allosteric protein. FDA thus has the potential to be a valuable tool in the investigation and rational design of mechanical properties in proteins and nano-materials.

Silk fiber mechanics from multiscale force distribution analysis.

Here we decipher the molecular determinants for the extreme toughness of spider silk fibers. Our bottom-up computational approach incorporates molecular dynamics and finite element simulations. Therefore, the approach allows the analysis of the internal strain distribution and load-carrying motifs in silk fibers on scales of both molecular and continuum mechanics. We thereby dissect the contributions from the nanoscale building blocks, the soft amorphous and the strong crystalline subunits, to silk fiber mechanics. We identify the amorphous subunits not only to give rise to high elasticity, but to also ensure efficient stress homogenization through the friction between entangled chains, which also allows the crystals to withstand stresses as high as 2 GPa in the context of the amorphous matrix. We show that the maximal toughness of silk is achieved at 10-40% crystallinity depending on the distribution of crystals in the fiber. We also determined a serial arrangement of the crystalline and amorphous subunits in lamellae to outperform a random or a parallel arrangement, putting forward what we believe to be a new structural model for silk and other semicrystalline materials. The multiscale approach, not requiring any empirical parameters, is applicable to other partially ordered polymeric systems. Hence, it is an efficient tool for the design of artificial silk fibers.

Dynamic allostery in the methionine repressor revealed by force distribution analysis.

Many fundamental cellular processes such as gene expression are tightly regulated by protein allostery. Allosteric signal propagation from the regulatory to the active site requires long-range communication, the molecular mechanism of which remains a matter of debate. A classical example for long-range allostery is the activation of the methionine repressor MetJ, a transcription factor. Binding of its co-repressor SAM increases its affinity for DNA several-fold, but has no visible conformational effect on its DNA binding interface. Our molecular dynamics simulations indicate correlated domain motions within MetJ, and quenching of these dynamics upon SAM binding entropically favors DNA binding. From monitoring conformational fluctuations alone, it is not obvious how the presence of SAM is communicated through the largely rigid core of MetJ and how SAM thereby is able to regulate MetJ dynamics. We here directly monitored the propagation of internal forces through the MetJ structure, instead of relying on conformational changes as conventionally done. Our force distribution analysis successfully revealed the molecular network for strain propagation, which connects collective domain motions through the protein core. Parts of the network are directly affected by SAM binding, giving rise to the observed quenching of fluctuations. Our results are in good agreement with experimental data. The force distribution analysis suggests itself as a valuable tool to gain insight into the molecular function of a whole class of allosteric proteins.

Mechanical response of silk crystalline units from force-distribution analysis.

The outstanding mechanical toughness of silk fibers is thought to be caused by embedded crystalline units acting as cross links of silk proteins in the fiber. Here, we examine the robustness of these highly ordered beta-sheet structures by molecular dynamics simulations and finite element analysis. Structural parameters and stress-strain relationships of four different models, from spider and Bombyx mori silk peptides, in antiparallel and parallel arrangement, were determined and found to be in good agreement with x-ray diffraction data. Rupture forces exceed those of any previously examined globular protein many times over, with spider silk (poly-alanine) slightly outperforming Bombyx mori silk ((Gly-Ala)(n)). All-atom force distribution analysis reveals both intrasheet hydrogen-bonding and intersheet side-chain interactions to contribute to stability to similar extent. In combination with finite element analysis of simplified beta-sheet skeletons, we could ascribe the distinct force distribution pattern of the antiparallel and parallel silk crystalline units to the difference in hydrogen-bond geometry, featuring an in-line or zigzag arrangement, respectively. Hydrogen-bond strength was higher in antiparallel models, and ultimately resulted in higher stiffness of the crystal, compensating the effect of the mechanically disadvantageous in-line hydrogen-bond geometry. Atomistic and coarse-grained force distribution patterns can thus explain differences in mechanical response of silk crystals, opening up the road to predict full fiber mechanics.

Mechanical network in titin immunoglobulin from force distribution analysis.

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.

pcaMethods--a bioconductor package providing PCA methods for incomplete data.

UNLABELLED: pcaMethods is a Bioconductor compliant library for computing principal component analysis (PCA) on incomplete data sets. The results can be analyzed directly or used to estimate missing values to enable the use of missing value sensitive statistical methods. The package was mainly developed with microarray and metabolite data sets in mind, but can be applied to any other incomplete data set as well. AVAILABILITY: http://www.bioconductor.org