Authors: Yann von Hansen¹, Michael Hinczewski^1,2, Roland R. Netz^1,3

1) Physics Department, Technical University of Munich
2) Institute for Physical Science and Technology, University of Maryland
3) Fachbereich Physik, Freie Universität Berlin

The concept of a protein diffusing in its free-energy folding landscape has been fruitful for both theory and experiment. Extensive all-atom simulations of small proteins and peptides in implicit and explicit solvent [1-3] have recently shown pronounced variations of the diffusivity – a measure of the internal friction arising from the transient breaking and reformation of bonds in the protein structure – along the reaction coordinate. Moreover, the analysis of the peptide kinetics in salt-solutions revealed that salt not only specifically modifies equilibrium properties (free-energy landscapes), but can also induce kinetic barriers due to individual ion binding, which are reflected in changes of the state-dependent diffusivity [3].

Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups the molecule is connected via linkers to a readout device, forming a mechanically coupled dynamic network. Deconvolution of equilibrium distributions, filtering out the influence of the linkers, is a straightforward and common practice [4-6]. We have developed an analogous dynamic deconvolution theory [7] for the more challenging task of extracting kinetic properties of individual components in networks of arbitrary complexity and topology. Our method determines the intrinsic linear response functions of a given object in the network, describing the power spectrum of conformational fluctuations. The practicality of our approach is demonstrated for the particular case of a protein linked via DNA handles to two optically trapped beads using Brownian dynamics simulations. Each well in the protein free energy landscape (corresponding to folded, unfolded, or possibly intermediate states) will have its own characteristic equilibrium fluctuations. The associated linear response function is rich in physical content, because it depends both on the shape of the well and its diffusivity.

References:
[1] G. Hummer, R. Best, Proc. Natl. Acad. Sci. USA 07, 1088 (2010)
[2] M. Hinczewski, Y. von Hansen, J. Dzubiella, R.R. Netz, J. Chem. Phys. 132, 245103 (2010)
[3] Y. von Hansen, I. Kalcher, J. Dzubiella, J. Phys. Chem. B 114, 13815 (2010)
[4] M.T. Woodside, S.M. Block et al., Science 314, 1001 (2006)
[5] M.T. Woodside, S.M. Block et al., Proc. Natl. Acad. Sci. USA 103, 6190 (2006)
[6] J.C.M. Gebhardt, T. Bornschlögl, M. Rief, Proc. Natl. Acad. Sci. USA 107, 2013 (2010)
[7] M. Hinczewski, Y. von Hansen, R.R. Netz, Proc. Natl. Acad. Sci. USA 107, 21493 (2010)