Protein Thermal Conductivity Measured in the Solid State Reveals Anharmonic Interactions of Vibrations in a Fractal Structure

Abstract

Energy processes and vibrations in biological macromolecules such as proteins ultimately dictate biological, chemical, and physical functions in living materials. These energetic vibrations in the ribbon-like motifs of proteins interact on self-similar structures and fractal-like objects over a range of length scales of the protein (a few angstroms to the size of the protein itself, a few nanometers). In fact, the fractal geometries of protein molecules create a complex network of vibrations; therefore, proteins represent an ideal material system to study the underlying mechanisms driving vibrational thermal transport in a dense, fractal network. However, experimental studies of thermal energy transport in proteins have been limited to dispersive protein suspensions, which limits the knowledge that can be extracted about how vibrational energy is transferred in a pure protein solid. We overcome this by synthesizing solid, water-insoluble protein films for thermal conductivity measurements via time-domain thermoreflectance. We measure the thermal conductivity of bovine serum albumin and myoglobin solid films over a range of temperatures from 77 to 296 K. These temperature trends indicate that anharmonic coupling of vibrations in the protein is contributing to thermal conductivity. This first-ever observation of anharmonic-like trends in the thermal conductivity of a fully dense protein forms the basis of validation of seminal theories of vibrational energy-transfer processes in fractal objects.

Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

“…53 This approach has been adopted to calculate thermal transport coefficients of aperiodic mesoscopic systems, including proteins. 4 Results for the latter compare reasonably well over a sizable range of temperature with calculations that incorporate anharmonic effects, 54,55 though anharmonicity contributes significantly to thermal transport coefficients around 300 K. 56 An additional approximation can be made to estimate local energy diffusion within a mesoscopic object. Communication maps are based on calculating first the heat current operator in harmonic approximation, then FIG.…”

Thermal Conductance across Phosphonic Acid Molecules and Interfaces: Ballistic versus Diffusive Vibrational Transport in Molecular Monolayers

“…[35][36][37][38][39]41 The temperature trends of the thermal conductance per unit area of the F21PA molecule suggest that thermal vibrations are interacting anharmonically in the molecule, consistent with previous analyses of the thermal conductivity trends in amorphous materials with complex unit cells, polymers and solid proteins. [78][79][80] To the best of our knowledge, this is the first observation of diffusive scattering of thermal vibrations in an interface-modifying molecule.…”

Intercalated water layers promote thermal dissipation at bio–nano interfaces

“…This result suggests that the presence of proteins does not significantly change the value of ITC. Previous studies reported that hydrogen bonds between proteins and intercalated water molecules are responsible for a promotion of interfacial thermal transport, which explains the fact that the protein–water interface (with hydrogen bonds) has a higher ITC of 100–300 MW m −2 K −1 than that for the octane–water interface (without hydrogen bonds), that is, 65 MW m −2 K −1 (refs 24 , 25 , 26 , 27 , 28 ). In our model, however, this effect is negligible because of the limited contact between intercalated water layer and protein.…”