# Out-of-equilibrium collective oscillation as phonon condensation in a model protein

## TL;DR

This paper models out-of-equilibrium collective oscillations in proteins as phonon condensation and confirms experimentally that proteins can exhibit such coherent oscillations when driven out of thermal equilibrium, linking theory and spectroscopy.

## Contribution

It introduces a classical phonon condensation model for protein oscillations and experimentally verifies this phenomenon using THz spectroscopy on BSA proteins.

## Key findings

- Observation of a 0.314 THz absorption feature in BSA under optical pumping
- Qualitative agreement between experimental data and the phonon condensation model
- Identification of collective molecular oscillation as the spectral feature

## Abstract

In the first part of the present paper (theoretical), the activation of out-of-equilibrium collective oscillations of a macromolecule is described as a classical phonon condensation phenomenon. If a macromolecule is modeled as an open system, that is, it is subjected to an external energy supply and is in contact with a thermal bath to dissipate the excess energy, the internal nonlinear couplings among the normal modes make the system undergo a non-equilibrium phase transition when the energy input rate exceeds a threshold value. This transition takes place between a state where the energy is incoherently distributed among the normal modes, to a state where the input energy is channeled into the lowest frequency mode entailing a coherent oscillation of the entire molecule. The model put forward in the present work is derived as the classical counterpart of a quantum model proposed long time ago by H. Fr\"ohlich in the attempt to explain the huge speed of enzymatic reactions. In the second part of the present paper (experimental), we show that such a phenomenon is actually possible. Two different and complementary THz near-field spectroscopic techniques, a plasmonic rectenna, and a micro-wire near-field probe, have been used in two different labs to get rid of artefacts. By considering a aqueous solution of a model protein, the BSA (Bovine Serum Albumin), we found that this protein displays a remarkable absorption feature around 0.314 THz, when driven in a stationary out-of-thermal equilibrium state by means of optical pumping. The experimental outcomes are in very good qualitative agreement with the theory developed in the first part, and in excellent quantitative agreement with a theoretical result allowing to identify the observed spectral feature with a collective oscillation of the entire molecule.