Out-of-Equilibrium Collective Oscillation as Phonon Condensation in a Model Protein

We describe the activation of out-of-equilibrium collective oscillations of a macromolecule 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 nonequilibrium 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 and 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 a long time ago by Frohlich in an attempt to explain the huge speed of enzymatic reactions. We show that such a phenomenon is actually possible. Two different and complementary THz near-field spectroscopic techniques-a plasmonic rectenna and a microwire near-field probe-have been used in two different labs to eliminate artifacts. By considering an aqueous solution of a model protein, the bovine serum albumin, we find 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 of the paper and in excellent quantitative agreement with the theoretical result, allowing us to identify the observed spectral feature with a collective oscillation of the entire molecule.