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Markus Meuwly and Peter Hamm: Temperature dependence of the heat diffusivity of proteins

In a combined experimental–theoretical study, we have investigated the transport of vibrational energy from the surrounding solvent into the interior of a heme protein, the sperm whale myoglobin double mutant L29W-S108L (left Figure [1]), and its dependence on temperature between 20 and 70 K [2]. The hindered libration of an unbound CO molecule trapped in one of the protein binding pockets (the Xe4 pocket) was used as the local thermometer. Energy was deposited into the solvent by IR excitation. Experimentally, the energy transfer rate increased from (30 ps)−1 at 20 K to (8 ps)−1 at 70 K. This temperature trend is opposite to what is expected, assuming that the mechanism of heat transport is similar to that in glasses. In order to elucidate the mechanism and its temperature dependence, nonequilibrium molecular dynamics (MD) simulations were performed. The simulations predicted an essentially temperature-independent rate of vibrational energy flow which is inconsistent with the experiments. We tentatively conclude that the MD potentials overestimate the coupling between the protein and the CO molecule, which appears to be the rate-limiting step in the real system at low temperatures. Assuming that this coupling is anharmonic in nature, the observed temperature trend can readily be explained.
In addition, a two-state model that had been proposed previously [1] to describe the motion of CO within the Xe4 pocket was re-examined. The double-well representation, exhibiting two roughly iso-energetic orientational minima of CO relative to the residues of the pocket had been used to derive an associated barrier to CO rotation.



We find [2] the model to be qualitatively consistent with population analysis of the orientation of CO projected onto the surface of a sphere during MD simulations (figure right). Additional local minima become visible in MD results and the relative energies of the two states were found to deviate significantly from the original symmetric-double-well interpretation. Simulations with more elaborate force fields are expected to provide more quantitative insights.

Top Figure: Left, Orientation of CO inside the Xe4 pocket of Myoglobin [1]. Stable orientational substates are explained in terms of different alignments of the CO dipole moment relative to the local electric field.

Top Figure: Right, a polar representation of the population of CO orientations inside the Xe4 pocket from MD simulations. High probability alignments are represented in red, low probability in blue. It is found that CO rotation is considerably hindered. At 100 K, one orientation is strongly favored while other local minima are also populated.

  1. Kriegl, J. M., Nienhaus, K., Deng, P., Fuchs, J., & Nienhaus, G. U. Ligand, "Dynamics in a Protein Internal Cavity", Proc. Natl. Acad. Sci., 100 (2003) 7069-7074.
  2. Helbing, J., Devereux, M., Nienhaus, K., Nienhaus, G.U., Hamm, P. & Meuwly, M., "Temperature Dependence of the Heat Diffusivity of Proteins", J. Phys. Chem. B, 116 (2012) 2620.

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