Neutron spin-echo studies of hemoglobin and myoglobin: multiscale internal dynamics

Neutron spin-echo spectroscopy was used to study structural fluctuations that occur in hemoglobin (Hb) and myoglobin (Mb) in solution. Using neutron spin-echo data up to a very high momentum transfer q ( approximately 0.62 A(-)(1)), we characterized the internal dynamics of these proteins at the levels of dynamic pair correlation function and self-correlation function in the time range of several picoseconds to a few nanoseconds. In the same protein solution, data transition from pair correlation motion to self-correlation motion as the momentum transfer q increases. At low q, coherent scattering dominates; at high q, observations are largely due to incoherent scattering. The low q data were interpreted in terms of an effective diffusion coefficient; on the other hand, the high q data were interpreted in terms of mean square displacements. Comparison of data from the two homologous proteins collected at different temperatures and protein concentrations was used to assess the contributions made by translational and rotational diffusion and internal modes of motion to the data. The temperature dependence of decay times can be attributed to changes in the viscosity and temperature of the solvent, as predicted by the Stokes-Einstein relationship. This is true for contributions from both diffusive and internal modes of motion, indicating an intimate relationship between the internal dynamics of the proteins and the viscosity of the solvent. Viscosity change associated with protein concentration can account for changes in diffusion observed at different concentrations, but is apparently not the only factor involved in the changes in internal dynamics observed with change in protein concentration. Data collected at high q indicate that internal modes in Mb are generally faster than those in Hb, perhaps due to the greater surface-to-volume ratio of Mb and the fact that surface groups tend to exhibit faster motion than buried groups. Comparison of data from Hb and data from Mb at low q indicates an unexpectedly rapid motion of Hb alphabeta dimers relative to one another. Dynamic motion of subunits is increasingly perceived as important to the allosteric behavior of Hb. Our data demonstrate that this motion is highly sensitive to protein concentration, temperature, and solvent viscosity, indicating that great care needs to be exercised in interpreting its effect on protein function.