Effect of molecular mass on the exponential time constant $τ ^$ . (A) $τ ^$ Values plotted as a function of the substrate molecular masses in log-log or linear scale (inset), ±95% confidence intervals. The fit to a power function is shown in a solid bold line; the thin gray lines indicate the power function at the 95% confidence intervals of the fit. (B) $τ ^$ Values as a function of the reporter molecular masses in log-log or linear scale (inset) for the joint set that includes our measurements as in A (blue) and the normalized $τ ^$ values that we computed for larger cargos, based on the reported ratio between nuclear and cytoplasmic fluorescence after incubation (Popken et al., 2015; red). The fit to a power function is indicated as in A. (C, top) The ratio between S_max, the sedimentation coefficient of a perfect sphere, and S, the measured sedimentation coefficient, plotted against the SAXS measured shape asymmetry. (bottom) The ratio between the measured sedimentation coefficient and the measured diffusion coefficient ± 95% confidence intervals, plotted against molecular mass. According to the theory of sedimentation, S/D ∼ molecular mass (Erickson, 2009). (D) S_max/S ratios, which are correlated with shape asymmetry plotted for reporter molecules of different molecular masses for the joint dataset as in B and C ± 95% confidence intervals. Enclosing envelopes (yellow surface representation) computed from either SAXS measurements for each substrate in our dataset, or modeled based on the S_max/S values in the Popken et al. (2015) datasets, using the crystallographic models of each of their GFP, PrA, and MBP subunits (Materials and methods). (E) Theoretical S_max and measured S sedimentation coefficients plotted as a function of τ in log-log scale. The fits of S_max and S to a power function of τ are shown in solid magenta and orange lines, respectively. (F) Same as inset of B, with a best fit to a theoretical model of an aqueous pore (Renkin, 1954) shown in solid magenta line.