Dynamics of proteins Mössbauer spectroscopy in energy and time K. Achterhold and F.G. Parak Physik-Department E17 Technische Universität München James-Franck Straße, D Garching, Germany

Proteins are the bricks of life. They function as enzymes, transport vehicles, storing container and as power stations to convert light into chemical energy. These skills are enabled by their structure and dynamics. An average structure is obtained by X-ray crystallography or NMR spectroscopy. The Mössbauer effect allows the study of protein dynamics. In iron containing proteins the iron is used as marker for the dynamics of the molecule. Mössbauer spectroscopy on 57 Fe has an energy resolution of 4.7 neV which corresponds to a time sensitivity for motions faster than 140ns. Rayleigh scattering of Mössbauer Radiation (RSMR) analysed with a Mössbauer absorber allows the determination of an average dynamics of the whole molecule even if it contains no Mössbauer nucleus. The density of phonons coupling to the iron can be determined by inelastic scattering of synchrotron radiation. A 57 Fe Mössbauer absorber in the scattered beam is only in resonance if phonons deliver or absorb the enery difference between the energy of the synchrotron beam and the Mössbauer resonance. An energy resolution of the synchrotron beam of 1 meV yields a time sensitivity with a lower limit of about 1ps. The oxygen storing protein myoglobin serves as a model for the investigation of the dynamics of  - helical proteins. Fig. 1 sketches the eight helices of sperm whale metmyoglobin and the heme group with the central iron atom. Fig. 1

Fig. 2 a) b) Fast processes: Phonons coupled to the heme iron. Anisotropic harmonic vibrations Phonon assisted Mössbauer effect with synchroton radiation on a single crystal of myoglobin is used to measure the anisotropic local vibrations of the iron. The two heme groups of the 2 molecules within the crystallographic unit cell are shown in Fig.2a along the c-axis and in Fig.2b along the b-axis. Blue arrows show 5 orientations of the incoming beam. Fig. 3 a) b) Fig.3 presents some results. The left column in Fig. 3a gives the scattering spectra for two selected orientations ( 30° and 120°). In the right column of Fig.3a the density of phonon states is extracted from the spectra. Red and blue marks two vibrational modes. A series of orientations can be fitted with a cos 2  -law and enables to extract the direction of vibration (Fig.3b). The vibration at 33 meV (marked in blue) is oriented parallel to the c-axis at  =0°. The mode at 22 meV is perpendicular to the heme. Achterhold, K., Keppler, C., Ostermann, A., van Bürck, U., Sturhahn, W., Alp, E.E. and Parak, F.G. (2002) Vibrational dynamics of myoglobin determined by Phonon assisted Mössbauer effect. Phys. Rev. E, 65,

Slow protein specific modes revealed by Mössbauer absorption spectroscopy Fig.4 A Mössbauer spectrum of metmyoglobin crystals at 295K is shown in Fig.4. It can not be fitted with Lorentzians of the typical line widts of 57 Fe (dashed line). At least one additional very broad line is necessary. The insets in Fig.5 demonstrate that broad lines are absent at low temperatures. Mean square displacements,, obtained from the area of the narrow lines increase linearly with temperature up to 180K. At higher temperatures a dramatic increase occures, and the broad lines become measurable. We attribute this behaviour to two types of motions. The - values are caused by solid state like vibrations and can be calculated from the density of phonon states or from a normal mode analysis. Above about 180K protein-specific modes start to contribute. Due to the high energy resolution of the Mössbauer spectroscopy the - values stem from motions faster than 140ns (compare time resolution in Fig.4). Fig.5

The broad lines indicate quasi diffusive motions. The analysis of these data together with the results of other experiments yields the following physical picture: Protein molecules can be in two types of states. At very low temperatures they Fig.6 are frozen in a „rigid state“ (conformational substates) where they perform harmonical motions. With increasing temperature the probability increases to reach a „ flexible state “ where segments of the molecules perform a Brownian motion in limited space. It should be mentioned that only molecules in the flexible state can perform a conformational change if e.g. the ligation changes. Parak, F.G. (2003) Physical aspects of protein dynamics. Rep. Progr. Phys., 66, Segmental motions determined by RSMR Fig.7 Mössbauer radiation of a 57 Co source is scattered by the sample. The scattered radiation is analysed by a Mössbauer absorber (Fig.7). From the inelastic scattering as function of the scattering angle one can estimate the size of the collectively scattering segments. In myoglobin they have the size of  -helices (Fig.8). Nienhaus, G.U., Hartmann, H., Parak, F., Heinzl, J. and Huenges, E. (1989) Angular dependent Rayleigh scattering of Mössbauer radiation on proteins. Hyperfine Interactions, 47, collective movement: total molecule  helices Fig.8