Tracking correlations of vibrational motion from biomolecular
solutes into the surrounding solvent
Matthias Heyden1
1
Max-Planck-Institute für Kohlenforschung, Theoretical Chemistry, Kaiser-Wilhelm-Platz 1,
45470 Mülheim an der Ruhr, Germany
1. Introduction
Solute-induced effects on the dynamics of solvating water molecules are commonly
considered as short-ranged. Experiments and simulations show that picosecond timescale
dynamical processes, such as hydrogen bond rearrangements, rotational relaxation and also
diffusion processes in the hydration water of various solutes are slowed down relative to bulk
and that these effects are restricted mostly to the first hydration layer, i.e. distances on the order
of 3 Å. The slower dynamics can be elegantly explained by increased solute-water hydrogen
bond strengths and the excluded volume of the solute, which protects direct solute-solvent
hydrogen bonds from other water molecules [1].
Molecular dynamics simulations demonstrate that such changes in picosecond dynamics are
often accompanied by a blue shift of vibrational frequencies in the far-infrared [2], which are
characteristic for the intermolecular vibrations of the water hydrogen bond network. While such
shifts in vibrational frequencies are again limited mainly to the first hydration layer, terahertz
spectroscopy experiments detect a long-ranged change in the hydration water absorption
coefficient, which extends ~10 Å into the surrounding solvent at frequencies between
2.2−2.6 THz [3].
Using atomistic molecular dynamics simulations and a specific methodology to analyze auto
and cross correlations of local time dependent fluctuations in real space, we are able to provide a
microscopic picture that explains these seemingly contradictory findings [4].
2. Results
To analyze local time dependent fluctuations and correlations between them, we introduce a
smooth density of weighted atomic velocities. This approach allows us to analyze in detail, for
example, correlated collective vibrational motion in the simulation, in particular between
biomolecular solutes and their surrounding hydration shell. While we can confirm, that
frequencies of intermolecular vibrations are essentially bulk-like for water molecules in the
second hydration shell, our results also show that the vibrations of water molecules in the
experimental frequency window are still correlated to the vibrational motion of solute surface
atoms at separation distances of up to 10 Å [4]. These correlations can be traced back to
collective modes that originate in vibrations of water molecules directly bound to the solute and
propagate into the surrounding hydration shell with velocities comparable to sound. We show,
that the chemical properties of the solute-water interface, e.g. the presence of solute-water
hydrogen bonds, affect specifically longitudinal collective modes and therefore indicate a nonuniform propagation of correlated vibrations into the hydration water of, e.g., proteins [4].
The long-ranged correlations can be described as ‘in-phase’ and ‘anti-phase’ vibrations of the
protein surface and the water molecules of the surrounding water hydrogen bond network. Their
sensitivity to the chemical properties of the solvent exposed protein surface, may let us speculate
about a potential role of such long-ranged solute-induced effects, e.g. in molecular recognition
events.
Figure 1: Illustration of the λ-repressor protein with a ~10 Å hydration shell (left) and spectra of mass weighted
velocity cross correlation functions (right) of non-hydrogen protein surface atoms and water oxygens resolved as a
function of inverse real space distance k=2π/r for different parts of the protein surface, as well as longitudinal (||) and
transverse (_|_) components [4].
3. Acknowledgements
M. H. acknowledges financial support from the German Academy of Sciences Leopoldina. This
work is supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche
Forschungsgemeinschaft.
4. References
[1] F. Sterpone, G. Stirnemann, J. T. Hynes and D. Laage, “Water Hydrogen-Bond Dynamics around Amino Acids:
The Key Role of Hydrophilic Hydrogen-Bond Acceptor Groups”, J. Phys. Chem. B 114, pp. 2083-2089
(2010).
[2] S. Chakraborty, S. K. Sinha, and S. Bandyopadhyay, “Low-Frequency Vibrational Spectrum of Water in the
Hydration Layer of a Protein:   A Molecular Dynamics Simulation Study”, J. Phys. Chem. B 111, pp. 1362613631 (2007).
[3] S. Ebbinghaus, S. J. Kim, M. Heyden, X. Yu, U. Heugen, M. Gruebele, D. M. Leitner and M. Havenith, “An
extended dynamical hydration shell around proteins”, Proc. Natl. Acad. Sci. 104, pp. 20749-20752 (2007).
[4] M. Heyden and D. J. Tobias, “Spatial Dependence of Protein-Water Collective Hydrogen-Bond Dynamics”,
Phys. Rev. Lett. 111, 218101 (2013).