Many biological processes such as cell proliferation and signaling are guided by mechanical stress. Proteins as the molecular machinery behind these processes are reacting on or withstanding mechanical forces in specific ways. How mechanical stress propagates through proteins to induce a certain mechanical response is currently unknown.

Within our group, I developed a new method that detects force distribution in proteins, reminiscent of computational
approaches used to engineer macroscopic structures. The method, termed "force distribution analysis (FDA)" is based on molecular dynamics simulations during which we calculate changes in inter-atomic forces.
Observing forces rather than coordinates allows us to visualize signal propagation in stiff materials, including crystals or crystalline protein units.
A real world example where observing forces is superior to observing coordinate changes is Newtons cradle (Figure 1). As the spheres in the middle hardly move, no coordinate change can be detected. Still, forces propagate through all of the spheres, and thus observing changes in forces will reveal the true propagation pathway.

Figure 1: Symbolic illustration of Newtons cradle. Spheres b and c do not move and thus signal propagation through them can only be detected when observing forces directly.

FDA can be applied to a wide range of proteins, including proteins bearing mechanical load as well as enzymes or transcription factors. In particular, we were successful in determining the origin of mechanical robustness in titin IG domains, common building blocks of human muscle fibers (Figure 2).

Figure 2: force distribution in immunoglobulin. The force distribution network spanning the IG domain is displayed as red edges. Force distribution was determined by pulling the protein with a constant force, as indicated. The levelplot shows force distribution along a cut through the center of the protein.



Protein evolution
An interesting question regarding the evolutionary design of proteins is, if evolutionary constraints resemble force distribution patterns in proteins. Hereto we statistically analyse co-evolution in protein families, using a standard approach termed "statistical coupling analysis (SCA)".
We were able to relate evolutionary constrains in titin IG domains (Figure 3) to the force distribution pattern observed within these domains.

Figure 3: Network of evolutionary coupled residues in Immunoglobulin. Evolutionary coupling means that two residues are statistically dependant during evolution. I.e. if residue A changes there is evolutionary pressure on residue B to change as well, in order to maintain the protein's function.


> Publications

W. Stacklies, F. Xia, F. Gräter. Dynamic Allostery in the Methionine Repressor revealed by force distribution analysis. PLoS Comp Biol, ACCEPTED

C. Baldauf, R. Schneppenheim, W. Stacklies, T. Obser, A. Pieconka, S. Schneppenheim, U. Budde, F. Gräter. Shear-Induced Unfolding Activates von Willebrand Factor A2 Domain for Proteolysis. Journal of Thrombosis and Haemostasis, ACCEPTED

S. Xiao, W. Stacklies, M. Cetinkaya, B. Markert, F. Gräter. Mechnical Response of Silk Crystalline Units from Force Distribution Analysis. Biophysical Journal, 96(10) 3997-4005 (2009)

W. Stacklies, M.C. Vega, M. Wilmanns and F. Gräter. Mechanical Network in Titin Immunoglobulin from Force Distribution Analysis. PLOS Comp. Biol. 5(3):e1000306 (2009) [pdf]

W. Stacklies, H. Redestig, M. Scholz, D. Walther and J. Selbig. pcaMethods - a bioconductor package providing PCA methods for incomplete data.  Bioinformatics 2007, 23(9):1164-1167
Download the pcaMethods package.