Debye-Waller factor proteins

Traditionally, x-ray spectroscopy measures an inhomogeneous distribution of structures, represented by the nuclear Debye Waller factors, and yields no information on the time scales of their rearrangements. Collective protein motions after fast optical triggers, on the other hand, have been studied with the help of pulsed synchrotron radiation with nanosecond time resolution (11). (See also Ref. 12 for a collection of review articles on time-resolved diffraction techniques.)... 

Here fl,- is the force constant for atom i and is the thermally averaged mean-square displacement for atom i in the protein the latter quantity is proportional to the crystallographically determined Debye-Waller factor if static disorder is neglected (see Chapt. VI). To simplify the treatment, average mean-square displacements can be used to represent the different types of atoms. The factor 5(r,) is an empirical scaling function that accounts for the interatomic screening of particles which are away from the RZ-RR boundary, 108 it varies from 0.5 at the reaction zone boundary to zero at the reaction region (see Fig. 8). 

However, low-temperature spectroscopy, in particular the fluorescence-narrowed emission, can in principle tell one further thing about the influence of proteins on chromophores. There can be a quasi-continuous tail at energies below the ZPL peak, and it represents coupling of the dipole transition to the low-frequency modes (the phonons) of the protein or the solvent. The relative strength of the ZPL to the phonon tail is the Debye-Waller factor and is a measure of the strength of the phonon-chro-mophore coupling. The phonon band is expected to be homogeneously broadened. Unfortunately, at this point no one has been able to use low-temperature spectroscopy to resolve the ZPL and the Debye spectrum in a protein, or observe the Debye factor as a function of temperature. We look forward to these important measurements. 

There is some evidence that the collective modes are coupled to the electronic transitions in proteins, although these measurements are somewhat indirect since no one has yet seen direct Debye-Waller factors in the ZPL fluorescence work. The main evidence has come from the work of Vos et al. involving electron transfer studies in photosynthetic reaction centers. Martin and collaborators have engineered a mutant of the photo-... 

Frauenfelder, H. (1989). The Debye-Waller factor from villain to hero in protein crystallography. International Journal of Quantitative Chemistry, 35, 711-15. 

Analysis of the Debye—Waller B factors suggests that 33—35 waters are strongly bound. These are located mostly at positions that are equivalent in the HL and TEWL structures. Hagler and Moult (1978) noted the similarity in water positions determined for two crystal forms, triclinic and tetragonal, of hen egg white lysozyme. The waters found for the hen egg white proteins are also largely equivalent to ones found for HL and TEWL. These observations suggest that essential features of the water structure in the crystal are intrinsic properties of the hydrated protein and would be found also in the solution state. 

Since atomic fluctuations are the basic elements of the dynamics of proteins (see Chapt. VI.A), it is important to have experimental tests of the accuracy of the simulation results. For the magnitudes of the motions, the most detailed data are provided, in principle, by an analysis of Debye-Waller or temperature factors obtained in crystallographic refinements of X-ray structure. 

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