Crowding and hydrodynamic interactions likely dominate in vivo macromolecular motion

Abstract

To begin to elucidate the principles of intermolecular dynamics in the crowded environment of cells, employing brownian dynamics (BD) simulations, we examined possible mechanism(s) responsible for the great reduction in diffusion constants of macromolecules in vivo from that at infinite dilution. In an Escherichia coli cytoplasm model comprised of 15 different macromolecule types at physiological concentrations, BD simulations of molecular-shaped and equivalent sphere representations were performed with a soft repulsive potential. At cellular concentrations, the calculated diffusion constant of GFP is much larger than experiment, with no significant shape dependence. Next, using the equivalent sphere system, hydrodynamic interactions (HI) were considered. Without adjustable parameters, the in vivo experimental GFP diffusion constant was reproduced. Finally, the effects of nonspecific attractive interactions were examined. The reduction in diffusivity is very sensitive to macromolecular radius with the motion of the largest macromolecules dramatically slowed down; this is not seen if HI dominate. In addition, long-lived clusters involving the largest macromolecules form if attractions dominate, whereas HI give rise to significant, size independent intermolecular dynamic correlations. These qualitative differences provide a testable means of differentiating the importance of HI vs. nonspecific attractive interactions on macromolecular motion in cells.

Fig. 1.

Molecular-shaped (left) and sphere (right) systems at 300 mg/mL. Macromolecules are represented in different colors. Figures were generated by VMD (56).

Fig. 2.

Long-time diffusion constant ratio as a function of macromolecule radius in the sphere (open symbols) and molecular-shaped systems (filled symbols) with steric repulsion. Squares, circles, and triangles are at 250, 300, and 350 mg/mL, respectively. The reductions in diffusion constant of GFP measured in vivo of DH5α (11), BL21(DE3) (12), and K-12 E. coli (12) are shown by plus, cross, and asterisk, respectively. Dashed line is GFP’s radius.

Fig. 3.

Reduction in diffusivity as a function of radius for the system with HI at three different concentrations. Triangles and circles represent D^S/D₀ and D^L/D₀, respectively. Open (filled) symbols are values in the sphere model with repulsive (HI) interactions. Plus, cross, and asterisk symbols are as in Fig. 2. Dashed line is GFP’s radius.

Fig. 4.

At 300 mg/mL, long-time diffusion constant ratio, D^L/D₀, as a function of radius in the nonspecific, van der Waals interaction (HI) model is represented by squares (filled circles). Dashed line is GFP’s radius.

Fig. 5.

Normalized pair correlation function, C_ij, averaged over GFP-GFP (left) and RNA polymerase-RNA polymerase (right) pairs for three different simulation models at 300 mg/mL. The Stokes radii of GFP and RNA polymerase are 24.0 and 66.5 Å, respectively.