Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Elastic and inelastic scattering of neutrons and X-raysPicosecond-Timescale Fluctuations of Proteins in GlassyMatrices: The Role of viscosityProteins perform most of the functions of livingthings. They are real nano-engines, whosefunctioning deserves to be studied in action.Actually, despite its importance, the precise natureof the internal motions of proteins remains amistery. In particular fast relaxations in thepicosecond-timescale play a key role for biologicalactivity. When proteins are embedded in glassymatrices both the onset and the amplitude of thesefluctuations appear to be driven by the environmentjust around the protein surface [1]. Here we report astudy performed via elastic neutron scatteringexperiments at the backscattering spectrometerIN13 [2]. In particular we investigated lysozyme, asimple model enzyme, in the hydrated powder stateand when it is plunged in different kind of glassymatrices, in the temperature range 20 ÷ 320 K. Thecalculated protein mean square displacements (MSD) follow a purely vibrational behaviour at lowtemperature.MSD show a temperature critical behaviour that istightly linked with that of η, with crucial changes justin proximity of the glass transition. Indeed, theinternal dynamics of proteins is strongly determinedby the ability of the surface protein side-chains tomove. If we describe the picosecond timescalemotions of a particle in terms of Brownian diffusion,then the Stokes-Einstein law leads to an inverserelationship between the relevant MSD and bulkviscosity ~η -1 . Actually, from our results itfollows that ~(logη) -1 . This weaker dependencecould be due to the fact that it is the microviscositysensed by the particle, possibly different from η,which is related to the corresponding dynamics. Inaddition, the evidence that both solvent and proteinMSD are related to η by the same functionaldependence indicates that the protein local dynamicsis closely coupled with that of the host. Thus ourfindings indicate that it is just the molecular networkimmediately around the protein surface to drive thefast fluctuations in proteins.log(η in Poise)1086420lysozyme+glycerol0h-20.42h0.83h-40 2 4 6 8 101/6 2w(Å -2 )Fig. 1. Logarithm of solvent bulk viscosity vs. theinverse of the protein double-well (relaxational)contribution to total mean square displacements (h =grams of water/grams of lysozyme).At around 100 K a gradual departure from thisvibrational behaviour takes place. This marks theonset of jumps from the ground to the excited statein a double-well model with corresponding MSD of 2w. In Fig. 1 we represent the logarithm of thebulk viscosity η of some glycerol-water mixtures vs.the inverse of 6 2w of lysozyme in thecorresponding glycerol-water matrices. Quitesurprisingly we observe that a linear relationshipexists in the whole investigated temperature range.We verified that such a law is obeyed in all thesystems we studied, as Fig. 2 shows. It should beremarked that the linear relationship between logηvs. 1/6 2w is satisfied also in some glass formers[3]. Anyway, in these materials it is the bulkviscosity and the fast dynamics of the same systemthat are correlated. What’s the meaning of therelationship we found in a complicated system suchas a protein in glassy environments? The existenceof a linear dependence tells us that protein relaxationlog(η in Poise)1412108642012 108641/6 2w(Å -2 )200.20.00.40.60.81.0 hFig. 2. The law logη ~ 1/6 2w is verified for allthe measured samples. Lysozyme at 0.3h (purple)and 0.4h (violet); lysozyme in glycerol at 0h (blue),0.2h (gray), 0.42h (red) and 0.83h (black);lysozyme in glucose at 0h (pink), 0.15h (orange),0.41h (dark green), 0.59h (cyan) and 0.71h (green).References[1] A. Paciaroni, S. Cinelli, G. Onori, Biophys. J. 83,1157 (2002).[2] E. Cornicchi, G. Onori and A. Paciaroni, Phys.Rev. Lett. 95, 158104 (2005).[3] U. Buchenau, and R. Zorn, Europhys. Lett. 18,523 (1992); J. C. Dyre and N. Boye Olsen, Phys.Rev. E 69, 042501 (2004) and references therein.AuthorsE. Cornicchi, G. Onori and A. PaciaroniDipartimento di Fisica, Università di Perugia, CRS-SOFT Unità di Perugia and Centro per i MaterialiInnovativi e Nanostrutturati (CEMIN), Via A. Pascoli,I-06123 Perugia, Italy.SOFT Scientific Report 2004-06102