Retrieving the intracellular topology from multi-scale protein mobility mapping in living cells

Abstract

In living cells, most proteins diffuse over distances of micrometres within seconds. Protein translocation is constrained due to the cellular organization into subcompartments that impose diffusion barriers and guide enzymatic activities to their targets. Here, we introduce an approach to retrieve structural features from the scale-dependent mobility of green fluorescent protein monomer and multimers in human cells. We measure protein transport simultaneously between hundreds of positions by multi-scale fluorescence cross-correlation spectroscopy using a line-illuminating confocal microscope. From these data we derive a quantitative model of the intracellular architecture that resembles a random obstacle network for diffusing proteins. This topology partitions the cellular content and increases the dwell time of proteins in their local environment. The accessibility of obstacle surfaces depends on protein size. Our method links multi-scale mobility measurements with a quantitative description of intracellular structure that can be applied to evaluate how drug-induced perturbations affect protein transport and interactions.

Figure 1. Parallelized acquisition of fluorescence signals for msFCCS analysis.

(a) Line illumination and parallelized multifocal fluorescence signal detection. Fluorescent proteins enter and leave the detection volumes by diffusion. The resulting local fluctuations in the fluorescence signal are detected on corresponding pixels of an EM-CCD camera array. (b) AC and XC analysis. By applying correlation analysis to the fluorescence signal recorded at a given detector pixel, AC curves can be calculated at every pixel position. Correlation of signals from spatially separated detection volumes are evaluated by computing XC curves (for example, signals of detection volumes 2 and 7 or detection volumes 2 and 17). These yield the MSD, the diffusion coefficient D and the concentration or molecule transmission rate as a function of the translocation distance d_n or translocation time τ_n. (c) AC curves or XC curves for a constant distance between detection elements are acquired along the illumination line and are visualized in so-called correlation carpets, from which diffusion barriers can be identified. (d) The diffusion coefficients determined for different distances can be used to reconstruct the molecules’ MSD as a function of the diffusion time t. The time dependence of the diffusion coefficient reflects the nanostructure ‘seen’ by the diffusing protein. Norm, normalized.

Figure 2. Instrument characterization, signal processing and validation of the data analysis pipeline.

(a) Approximation of the PSF of the line-confocal microscope as used for subsequent correlation analysis. (b) Fluorescence signal correction by Fourier filtering. Left: exemplary raw and corrected Fourier transformed fluorescence signal in the frequency domain. Right: fluorescence signal before and after signal correction in the time domain. (c) Experimental AC curve and XC curves for 1 and 3 μm diffusion distance for a reference measurement with 20 nM QDots in aqueous solution. Correlation curves were fitted with Supplementary Equation (22). (d) Experimental AC and XC carpet (3 μm) of QDots measured in water. (e) The MSD scales linearly with time for the QDot reference measurements in water as expected for free diffusion. Data are mean values ±s.e.m. (n=10 measurements). Norm., normalized.

Figure 3. Diffusion coefficients, trapped protein fractions and diffusion barrier density determined for GFP in living cells.

(a) Histograms for the retardation coefficient R_AC=D_AC/D (n>200 values). The parameter R_AC corresponds to the translocation time of GFP monomer (GFP₁), trimer (GFP₃) and pentamer (GFP₅) molecules relative to the average value obtained from the AC analysis. Measurements were conducted at about 50 positions equally distributed on a 10 μm long line for separation distances of 0 μm (AC), 0.6 μm and 1.2 μm (XC) in water, the nucleus and the cytoplasm. (b) FRAP measurements of RFP₁ (n=12 cells), GFP₃ (n=13 cells) and GFP₅ (n=12 cells). The fraction of trapped protein f_trap was obtained from the fit of either the post-bleach radial intensity profile after 100 ms with Supplementary Equation (29) (top row) or the average recovery curve with Supplementary Equation (30) (bottom row). Diffusion coefficients were determined from the average recovery curves. Data are mean values, error bars represent s.e.m. (c) Representative AC and XC carpets (0 μm, 0.6 μm and 1.2 μm separation distance) for GFP₁ in water, nucleus and cytoplasm. Regions with diffusion barriers can be identified from the fold increase of the translocation time ΔR plotted below the carpets. Negative ΔR values correspond to a decrease of the translocation time. An example for a diffusion barrier that is most pronounced for the 0.6 μm separation distance is marked with an arrowhead. Norm., normalized.

Figure 4. Measurements on multiple length scales by msFCCS.

(a) Line-confocal fluorescence images of representative U2OS cells expressing GFP₁, GFP₃ and GFP₅. The line positions for the measurement of AC and spatial XC functions in homogeneous regions of the nucleus and cytoplasm are indicated. (b) Representative average AC (0 μm) and XC (1.6 and 3 μm) curves obtained in cytoplasm (red) and nucleus (blue). For large diffusion distances, distinct peaks were visible in the diffusion time distributions that shift to larger translocation times for increasing diffusion distance. Solid lines represent the fitted model functions given by Supplementary Equation (22). Scale bar, 5 μm. Cyt, cytoplasm; Nuc, nucleus; Norm, normalized.

Figure 5. Parameters for intracellular topology from time dependence of diffusion coefficients.

(a) Average scale-dependent mobility of GFP₁ (Nuc: n=14 cells, Cyt: n=13 cells), GFP₃ (Nuc: n=16 cells, Cyt: n=15 cells) and GFP₅ (Nuc: n=18 cells, Cyt: n=18 cells) in the nucleus and cytoplasm. The time and length scale-dependent protein mobility is represented as the MSD (top row) or as the time-dependent diffusion coefficient D(t) in double-logarithmic representation (bottom row). Data are mean values±s.e.m. The solid lines represent a fit according to the random obstacle model in Equation (1). (b) Time-dependent diffusion coefficients were well described by a model for diffusion in a random porous medium. On small scales, molecules diffuse freely with D₀ (left). At a characteristic distance λ, they collide with an immobile obstacle. On large scales, this collision–diffusion process can be described with a reduced diffusion coefficient D_∞. The parameters of the model function used for fitting the time-dependent diffusion coefficient in porous media are illustrated in double-logarithmic representation (right). The initial slope of the curve is related to the surface-to-volume ratio S/V (ref. 6). Extrapolation to short time scales yields the microscopic diffusion coefficient D₀ that would be measured in free solution, and extrapolation to large time scales yields the macroscopic diffusion coefficient D_∞ for translocations on large length scales. The ratio between both diffusion coefficients is referred to as retardation R. Based on these fit parameters, the correlation length λ can be calculated, which represents the length scale above which the medium appears homogeneous if it is sampled by a tracer of a given size. (c) Parameters characterizing the cellular environment derived from the fits of the time-dependent mobility of GFP multimers are the cellular viscosity η_app/η_H2O relative to water, the surface-to-volume ratio S/V that is a measure for the apparent obstacle concentration and the retardation R=D₀/D_∞. The dependence of R on the molecule size can be computed for polymeric obstacles to yield estimates for the average fibre diameter d_fiber and the obstacle volume fraction Φ₀ (ref. 30). Data are mean values±s.e.m. Dashed lines represent fitted model functions given by Supplementary Equation (34).

Figure 6. Mobility of GFP₃ in the cytoplasm after disassembly of cytoskeletal filaments.

Time-dependent diffusion coefficients measured in U2OS cells after perturbation of the cytoskeleton (red) compared with that in unperturbed cells (black, n=19 cells). (a) Disruption of actin microfilaments by cytochalasin D (n=15 cells). (b) Disruption of vimentin filaments by withaferin A (n=16 cells). (c) Disruption of microtubules by nocodazole (n=14 cells). Data are mean values±s.e.m., fit curves correspond to Equation (1). Perturbations were validated based on the distribution of fluorescently tagged β-actin, vimentin or microtubule-associated protein 4 (MAP4), respectively. Scale bar, 10 μm.

Figure 7. Mobility of GFP₃ in the nucleus after decondensation of chromatin.

(a) Time-dependent diffusion coefficient of inert GFP₃ in the nucleus of U2OS cells after perturbation of the chromatin structure with TSA (blue, n=15 cells) compared with that in unperturbed cells (black, n=16 cells). (b) Same as in a but after perturbation with CQ (blue, n=13 cells). (c) Mobility of STAT2 (red, n=12 cells), GFP₃ (white, n=15 cells) and GFP₅ (black, n=18 cells) in the cytoplasm of U2OS cells. The STFM image shows a representative cell expressing GFP-tagged STAT2. (d) Mobility of the chromodomain (CD) of HP1β in the cytoplasm (red, n=11 cells) and nucleus (blue, n=11 cells) compared with that of cytoplasmic GFP₁ (black, n=13 cells). The STFM image shows a representative cell expressing GFP-tagged CD. Data are mean values±s.e.m., fit curves correspond to Equation (1). Scale bar, 5 μm.

Figure 8. The cellular interior appears as a porous medium formed by random obstacles.

The correlation length λ for the distance between obstacles ‘sensed’ by a given protein is derived from the time dependence of its diffusion coefficient (Fig. 5).The parameter χ~15 nm is the estimated throat size of small pores that confine regions in the nucleus where GFP₅ (hydrodynamic radius r_H≈7.9 nm) is trapped while GFP₃ (r_H≈5.5 nm) remains mobile. Drug treatment induced structural changes as depicted on the right side of the scheme. Disassembly of cytoplasmic filaments resulted in a moderate increase of GFP₃ mobility (Fig. 6, Table 2). In contrast, chromatin decondensation increased GFP₃ mobility considerably (Fig. 7a,b, Table 2). Thus, chromatin is the major obstacle in the nucleus, whereas in the cytoplasm the cytoskeleton represents only one obstacle among others.