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.

Human centrin 2 (HsCen2) is a member of the EF-hand superfamily of calcium-binding proteins, often associated with the centrosomes and basal bodies. These organelles exhibit different morphological aspects, including a variety of centrin-containing fibers that connect the two centrioles or other structural elements of the pericentriolar space. The molecular basis of the Ca 2؉ -sensitive fibers and their precise role in centrosome duplication are not known. To explore the possible structural role of HsCen2, we initiated a physicochemical study of the self-assembly properties of the purified protein in vitro. Using light scattering experiments, we investigated the temporal evolution of the assembly process and characterized the dependence on various chemical and physical factors, including temperature, di-cation concentration, ionic strength, protein concentration, and pH. The reversible self-assembly revealed many features of a large-size protein polymerization, with nucleation and elongation steps. Kinetic and equilibrium experiments show that a hydrophobic fluorescent probe (ANS) inhibits the polymerization by interfering with the nucleation step, probably through interactions with the apolar exposed sites on the protein surface. A truncated form of HsCen2, lacking the first 25 residues (⌬25HsCen2), shows no detectable self-assembly, pointing to the critical role played by the N-terminal fragment in the supermolecular organization of HsCen2. As revealed by isothermal titration experiments, the isolated N-terminal domains bind with a significant affinity (2 ؋ 10 5 M ؊1 ) to preformed oligomers of ⌬25HsCen2 through an entropy-driven mechanism.

Translational and rotational diffusion coefficients of proteins in solution strongly deviate from the Stokes-Einstein laws when the ambient viscosity is induced by macromolecular co-solutes rather than by a solvent of negligible size as was assumed by A. Einstein one century ago for deriving the laws of Brownian motion and diffusion. Rotational and translational motions experience different micro viscosities and both become a function of the size ratio of protein and macromolecular co-solute. Possible consequences upon fluorescence spectroscopy observations of diffusing proteins within living cells are discussed.