The Stokes-Einstein-Debye equation is currently used to obtain information on protein size or on local viscosity from the measurement of the rotational correlation time. However, the implicit assumptions of a continuous and homogeneous solvent do not hold either in vivo, because of the high density of macromolecules, or in vitro, where viscosity is adjusted by adding viscous cosolvents of various size. To quantify the consequence of nonhomogeneity, we have measured the rotational Brownian motion of three globular proteins with molecular mass from 66 to 4000 kD in presence of 1.5 to 2000 kD dextrans as viscous cosolvents. Our results indicate that the linear viscosity dependence of the Stokes-Einstein relation must be replaced by a power law to describe the rotational Brownian motion of proteins in a macromolecular environment. The exponent of the power law expresses the fact that the protein experiences only a fraction of the hydrodynamic interactions of macromolecular cosolvents. An explicit expression of the exponent in terms of protein size and cosolvent's mass is obtained, permitting definition of a microscopic viscosity. Experimental data suggest that a similar effective microviscosity should be introduced in Kramers' equation describing protein reaction rates.

Laser photodissociation of respiratory proteins is followed by fast geminate recombination competing with escape of the oxygen molecule into the solvent. The escape rate from myoglobin or hemerythrin has been shown previously to exhibit a reciprocal power-law dependence on viscosity. We have reinvestigated oxygen escape from hemerythrin using a number of viscous cosolvents of varying molecular weight, from glycerol to dextrans up to 500 kDa. In isoviscous solutions, the strong viscosity dependence observed with small cosolvents is progressively reduced upon increasing the cosolvent's molecular weight and disappears at molecular weights greater than about 100 kDa. Thus, viscosity is not a suitable independent parameter to describe the data. The power of the viscosity dependence of the rate coefficient is shown here to be a function of the cosolvent's molecular weight, suggesting that local protein-solvent interactions rather than bulky viscosity are affecting protein dynamics.

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Evidence for ligand migration toward the xenon-binding cavities in myoglobin comes from a number of laser photolysis studies of MbO2 including mutants and from cryo- and time-resolved crystallography of MbCO. To explore ligand migration in greater detail, we investigated the rebinding kinetics of both MbO2 and MbCO under a xenon partial pressure ranging from 1 to 16 atm over the temperature range (293-77 K). Below 180 K xenon affects to a significant, but minor, extent the thermodynamic parameters for rebinding from the primary docking site in each Mb taxonomic substate. Above 200 K the ligand migrates to the proximal Xe1 site but when the latter is occupied by xenon a new kinetic process appears. It is attributed to rebinding from transient docking sites located on the path between the primary and the secondary docking site of both ligands. Ligand escape exhibits a more complicated pattern than expected. At room temperature O2 and CO escape appears to take place exclusively from the primary site. In contrast, at T approximately 250 K, roughly 50% of the CO molecules that have escaped from the protein originate from the Xe1 secondary site.