Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells

Abstract

Macromolecular crowding dramatically affects cellular processes such as protein folding and assembly, regulation of metabolic pathways, and condensation of DNA. Despite increased attention, we still lack a definition for how crowded a heterogeneous environment is at the molecular scale and how this manifests in basic physical phenomena like diffusion. Here, we show by means of fluorescence correlation spectroscopy and computer simulations that crowding manifests itself through the emergence of anomalous subdiffusion of cytoplasmic macromolecules. In other words, the mean square displacement of a protein will grow less than linear in time and the degree of this anomality depends on the size and conformation of the traced particle and on the total protein concentration of the solution. We therefore propose that the anomality of the diffusion can be used as a quantifiable measure for the crowdedness of the cytoplasm at the molecular scale.

FIGURE 1

The autocorrelation curve C(τ) obtained for subdiffusive motion in the framework of a FFPE (α_FPE = 0.65, open symbols) is well described by a fit with Eq. 1 (α_fit = 0.59, full line). (Inset) The actual value α_fit for the anomality obtained by this fitting (closed symbols) slightly deviates from the value α_FPE imposed in the FFPE (dashed line). The dependence is best described by α_fit = 1.1α_FPE − 0.12 (full line).

FIGURE 2

Representative autocorrelation curves for dextran in PBS (squares, triangles, diamonds: molecular masses m = 10 kDa, 150 kDa, 2 MDa, respectively). Best fits according to Eq. 1 (full lines) always resulted in α ≈ 1, indicating normal diffusion. (Inset) The hydrodynamic radius r_H as extracted from the diffusive time τ_D of the autocorrelation decay increases approximately as r_H ∼ m^0.4 (dashed line).

FIGURE 3

Representative autocorrelation curves for dextran in the cytoplasm of living cells in interphase (squares, triangles, diamonds: molecular masses 10 kDa, 150 kDa, 2 MDa, respectively). Best fits according to Eq. 1 (full lines) revealed that all dextrans moved subdiffusively (α = 0.86, 0.74, 0.64; from left). (Inset) A FITC-labeled IgG antibody (m = 150 kDa, r_H ≈ 5.5 nm) also showed strong subdiffusion (α ≈ 0.55).

FIGURE 4

(a) The distribution p(m) of protein masses m in the cytoplasm of HeLa cells (see Methods) is well described by a Poissonian (dashed line, mean 〈m〉 = 80 kDa). Due to the denaturing conditions of the gel, the fraction of low protein masses is overestimated and can be expected to be significantly higher in reality. (b) Average mean square displacement v(t) for globular proteins with radii 2 nm, 3.6 nm, and 5.4 nm (from top) as obtained by simulations using a Poissonian weight distribution (mean 〈m〉 = 350 kDa to soften the overestimation of low masses). The proteins occupied a fractional volume of 13%. Dashed lines highlight the power-law increase v(t) ∼ t^α. (c) Using the same parameters, the anomality parameter α is seen to decrease for increasing particle radii r. The full line is a guide to the eye. (d) Same as in (c) for a uniform distribution of molecular weights (50 kDa ≤ m ≤ 1MDa). Here, a similar decrease of α is observed, yet it occurs for higher values of r and a lower fractional volume occupied by the proteins (7%).

FIGURE 5

(a) Representative autocorrelation curves for 10 kDa dextran in solutions with different crowdedness due to dissolved unlabeled dextran (0.08 and 0.25 g/ml, from left). A shift and stretching of C(τ) is visible for increasing crowdedness. (b) Same as in a but for 500 kDa dextran. (c) The anomality parameter α decreases with increasing crowdedness as measured by the macromolecular concentration (diamonds, 10 kDa; asterisks, 40 kDa; squares, 500 kDa). (d) The diffusive time τ_D concomitantly increases with increasing macromolecular concentration, indicating an increase of the effective viscosity. For better visibility error bars have been omitted.