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

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. Fröhlich 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. * Electronic address: i.

Quantum Fluctuations in the Fröhlich Condensate of Molecular Vibrations Driven Far From Equilibrium

“…The equation for n 0 has a structure which is a reminiscence of the photon number for a single mode laser. Further simplification neglects the fluctuation of n 0 , namely, n 2 0 ≃ n 0 2 , which gives the steady-state phonon number at mode ω 0 shown in Fig.3(a) where the parameters are taken from recent experiment [27]. Moreover, the expansion n 0 in terms of r − r c leads to the scaling n 0 ≃ F 0 + F 1 (r − r c ) when approaching the critical point r = r c .…”

“…It seems plausible to attribute this phenomena to Fröhlich condensate that causes non-thermal distribution. The most recent experiment demonstrated in BSA protein the remarkable absorption feature around 0.314THz, when driving the system by optical pumping [27]. Understanding these interesting and intriguing experiments will lead us to the deep thinking about Fröhlich's mechanism, since the cooperativity has been shown to exist in some non-physical systems [28,29].…”

Collective Excitations in α-helical Protein Structures Interacting with the Water Environment

“…In recent intriguing work, the joint theoretical and experimental investigation of out-of-equilibrium collective oscillation of the Fröhlich type was carried out in the bovine serum albumin (BSA), the protein mainly composed of α-helical structures (Nardecchia et al, 2018). Note, that the resonance absorption spectrum in the terahertz frequency region for αhelical protein structures was defined by one of the authors (VNK) in the framework of the quantum mechanical model which describes the direct transfer of electron captured by the moving acoustic soliton (electrsoliton) along the molecular chain (Kadantsev and Savin, 1997).…”

“…Thus, excitation of the Fröhlich mode, in the form of the coherent dynamic structure, can be considered as the emergence of a spacetemporal dissipative structure in according to Prigogine's theory (Prigogine and Lefever, 1973) which is governed by the self-organization principals of Haken's synergetics in non-linear systems (Haken, 1983). At present, further investigation of the Fröhlich condensation in quantum dynamics and quasi-classical approaches were undertaken in order to determine the physical conditions of phonon condensation in proteins functioning far from thermal equilibrium (Vasconcellos et al, 2012), (Salari et al, 2011), (Preto, 2017), (Reimers et al, 2009), (Nardecchia et al, 2018).…”

A distributed lattice of aligned atoms exists in a protein structure: A hierarchical clustering study of displacement parameters in bovine trypsin

“…(11) Continuous excitation of fluorophore-labelled bovine serum albumin with visible light has resulted in a terahertz spectral signal, which evolved over minutes time scales. (12) Dynamics also plays a role in long-range allosteric effects as shown by NMR experiments. (13)(14)(15) It is frequently observed that a mutation or binding of a small molecule at one site can affect the dynamics at remote sites.…”