Hydrodynamics of segmentally flexible macromolecules

Abstract

Segmentally flexible macromolecules are composed of a few rigid subunits linked by joints which are more or less flexible. The dynamics in solution of this type of macromolecule present special aspects that are reviewed here. Three alternative approaches are described. One is the rigid-body treatment, which is shown to be valid for overall dynamic properties such as translational diffusion and intrinsic viscosity. Another approach is the Harvey-Wegener treatment, which is particularly suited for rotational diffusion. The simplest version of this treatment, which ignores hydrodynamic interaction (HI) effects, is found to be quite accurate when compared to a more rigorous version including HI. A third approach is the Brownian dynamics simulation that, albeit at some computational cost, might describe rigorously cases of arbitrary complexity. This technique has been used to test the approximations in the rigid-body and Harvey-Wegener treatments, thus allowing a better understanding of their validity. Brownian trajectories of simplified models such as the trumbbell and the broken rod have been simulated. The comparison of the decay rates of some correlation functions with the predictions of the two treatments leads to a general conclusion: the Harvey-Wegener treatment determines the initial rate, while the long-time behavior is dominated by the rigid-body relaxation time. As an example of application to a specific biological macromolecule, we present a simulation of an immunoglobulin molecule, showing how Brownian Dynamics can be used to predict rotational and internal dynamics. Another typical example is myosin. Literature data of hydrodynamic properties of whole myosin and the myosin rod are compared with predictions from the Harvey-Wegener and rigid-body treatments. The present situation of the problem on myosin flexibility is analyzed, and some indications are given for future experimental and simulation work.

Biomolecular hydration: From water dynamics to hydrodynamics

“…The present calculations, like previous ones (11,12,15), demonstrate that molecular hydrodynamics calculations with a fixed (protein-independent) effective atomic radius H can reproduce experimentally determined rotational diffusion coefficients. Our calculations yield H ϭ 0.30 nm.…”

“…The larger effective radius obtained there may reflect differences in the experimental data. In the previous analysis, the remaining difference between D R expt and D R calc was attributed to experimental error (15). We believe that two additional factors play a role here.…”

“…1 (15). The larger effective radius obtained there may reflect differences in the experimental data.…”

“…The theory proposed here was tested against a set of 16 proteins, for which D R has been determined from measurements of the backbone 15 N T 1 and T 2 relaxation times and the 15 NO{ 1 H} steady-state nuclear Overhauser effect. The protocols used for such relaxation experiments and the associated data analysis are highly standardized.…”

“…Typically, the calculated rotational diffusion coefficient is still 30% too large. This discrepancy, which exceeds the experimental uncertainty in D R by an order of magnitude, is usually ascribed to about half a monolayer of ''tightly bound'' water molecules (9)(10)(11)(12)(13)(14)(15)(16)(17).…”