Fluorescence loss in photobleaching (FLIP) is a dynamic imaging technique with the potential to include spatial information into analysis of protein dynamics, but this potential has not been explored. By treating images as data arrays rather than pictures, we present two FLIP analysis methods for assessing intracellular transport dynamics of fluorescent proteins. Our first approach comprises fitting a StrExp function to FL kinetics on a pixel-by-pixel basis. The rationale behind this idea is that the time-dependent rate coefficient of the StrExp function is suitable to describe transport under conditions, where the “well-stirred compartment” assumption fails. Diffusion gradients or topological constraints cause deviation from the concept of compartment homogeneity, and that can be modelled with differential equations having time-dependent rate coefficients [35
]. The StrExp function is based on such an equation, and our method of pixel-wise fitting this function to FLIP image sets provides kinetic maps of locally heterogeneous transport and allows for exact data reconstruction using the derived model parameters (for example, see Figure A). FLIP as an imaging method, has the advantage that the user can determine the time resolution of the experiment by setting pauses of arbitrary length between individual bleaches. For short pauses, i.e., fast repeated bleaching; FLIP-experiments might become diffusion-limited (see Figures , and and Additional file 1
: Figure S1, S2 and S3). We demonstrate on simulated and experimental FLIP image sets that a spatial gradient of the fitting parameters (i.e., stretching, h
, and time or rate constant, respectively) of the StrExp function is characteristic for a diffusion-limited FLIP experiment.
For larger pauses between the bleaches, eventual hindrance to diffusion due to transient binding or barriers can be detected on the sub-cellular level by pixel-wise FLIP analysis without pre-selection of ROIs (Figures and ). This result is not in line with isotropic normal diffusion of eGFP in cells, though eGFP is known to show minimal interaction with its surroundings [49
]. An often (but not always, see [50
]) overlooked aspect in the literature of biophysical diffusion studies (for example using FRAP) is that not only homogenous diffusion but also locally heterogeneous diffusion (i.e., with a space-dependent diffusion constant) with continuity between the regions of varying D will cause an equilibration of any concentration gradient. This is illustrated in the simulation shown in Figure (see above). Thus, already the initial distribution of eGFP in the prebleach image tells us that crowding effects exclude eGFP from some regions in the nucleus and the cytoplasm. We are aware of one recent study, where the structured fluorescence intensity of an inert fluorescent protein (i.e., yellow fluorescent protein, YFP) in a single image of the cell has been ascribed to the cytoplasm and nucleoplasm being an ‘effective porous medium’ [50
]. In porous media, one distinguishes diffusion in the liquid phase (here the cytosol or nucleosol) from that in the medium with constrained motion. We speculate that the large variation in rate coefficients, we find for FLIP data of eGFP in the cytoplasm is a consequence of this porosity. Since the optical resolution of the confocal microscope (i.e., about 250 nm) is several times larger than the pore size of the cytoplasm (i.e., 30–100 nm), one cannot segment this cytoplasmic ultrastructure, though it obstructs protein motion [51
]. Furthermore, even for ‘inert’ biomolecules lacking specific interactions, like eGFP, not only obstruction is found but also enhancement of diffusion could be triggered by active transport of other components causing enforced motor activity and dynamic remodelling of the cytoskeleton network [52
]. Thus, the cytosol might provide rapid decay channels for eGFP, while the high protein concentration, organelles and cytoskeleton constrain eGFP mobility otherwise. Rapid decay channels can be detected with the StrExp fit to FLIP data as individual pixels with high rate coefficients, even far from the bleached ROI (see Figures and and Additional file 4
: Movie S3). Additional simulations of binding-barrier-limited FLIP experiments using the compartment model of Equations. 3–5 but with rate constants varying on a pixel-by-pixel basis were performed to account for spatial heterogeneity (Additional file 1
: Figures S7 and S8). By fitting the StrExp function to these simulated time courses, we found local variation of the recovered parameters (i.e. h
-map and time constant map), but in a much narrower range than observed for the FLIP data for eGFP in cells (compare Figure and with Additional file 1
: Figure S8). Thus, transport of eGFP as measured by FLIP follows a complex dynamic relaxation pattern due to local hindrance to diffusion on one hand and local enhancement of diffusive transport on the other. Such complex behaviour cannot be understood from a simple binding-barrier or diffusion model of intracellular transport but it can be revealed using pixel-wise fitting of the StrExp function to FLIP image sets.
Using our quantitative FLIP analysis, we could also visualize local diffusion barriers for eGFP in the nucleus (see Figures , and Additional file 1
: Figure S9). These kinetic domains in the nucleus are likely a consequence of the fractal chromatin organization [53
]. Recent results published by Gratton and co-workers detect also barriers for eGFP diffusion in the nucleus of CHO cells using pair correlation functions (pCF) [54
]. An advantage of their method is the ability to extract local diffusion coefficients directly from the cross-correlation of intensity fluctuations of the same fluorophore at two different but adjacent points in the sample [55
]. Rare intensity bursts report on eGFP molecules travelling across regions with strongly varying DNA density [54
]. The pCF method has also been applied to study transport of eGFP between nucleus and cytoplasm, where the nuclear membrane including the NPC appeared as obstacle to eGFP inter-compartment diffusion [56
]. This diffusion barrier is nicely detected in the time constant map of our quantitative pixel-based FLIP analysis (see Figure G, J), suggesting that fluorescence fluctuation techniques like pCF and our approach provide complementary information.
To the best of our knowledge, there is only one full publication published this year, which also applies a pixel-wise regression of a decay function to FL data of FLIP image sets [23
]. Lelieveldt and colleagues assumed a simple exponential decay of the FL allowing for linear regression in the logarithmic space. They also performed a noise reduction as pre-processing step and were able to correct for sudden motion of the specimen or the image field during acquisition of the FLIP data [23
]. Our approach implemented in ‘PixBleach’ uses a Gaussian filtering in the space and time domain as pre-processing step which corrects in our hands sufficiently for image noise and for small movements (in a range of one or two pixels) [40
]. Since we apply a motion correction as pre-processing step in case of larger displacement, no further corrections were necessary for the image data used here (see Methods section and [57
]). Using the StrExp function is clearly superior to simple mono- or bi-exponential decay models, since it can model FL inside and outside the bleached region for both, binding/barrier- and diffusion-limited FLIP experiments. The delayed decay described by a compressed exponential function as a consequence of binding or barriers (in binding/barrier -limited FLIP experiments) or due to long distance to the bleached area (in diffusion-limited FLIP experiments) cannot be adequately described with simple exponential decay functions (see Table ).
Quantitative FLIP microscopy should also be a method to compare results from different cells. This, however, is not possible with the pixel-based FLIP analysis, because the kinetic parameters recovered from the StrExp fit to data are a function of the total amount of fluorophore in a given cell, the diameter of the bleach spot and the length of the pauses between bleaches. The empirical StrExp fitting function only provides information about the nature of the observed transport process (e.g. diffusion- or binding-limited, see Table ) and about local variation in transport dynamics for a given experiment and cell. Experiment-independent binding and dissociation parameters of a fluorescent protein can therefore not be measured by this approach. To overcome this limitation, we developed a complementary method based on compartment modelling of FLIP data and applied it to determine local heterogeneity in intracellular protein aggregation. Such aggregation is observed in cellular models of various neurodegenerative diseases [45
]. Since protein aggregates tend to move during FLIP experiments, we combine tracking of individual IB’s containing mtHtt with extended polyQ repeat (eGFP-Q73) with non-linear regression of an analytical MC model to the FLIP-induced intensity decay in these structures (Figures , ). This enables us to measure mobility parameters, like diffusion constants from the calculated MSD and to determine in parallel association and dissociation rate constants for eGFP-mtHtt from the measured FL kinetics in IB’s. Thus, we demonstrate that mtHtt in IB’s can exchange with mtHtt in the cytoplasm in agreement with earlier observations for other polyQ diseases [43
]. Using our MC modeling strategy, we can derive for the first time in-vivo binding parameters of eGFP-mtHtt showing that the exchange takes place with a half-time of 2–4 min. Since MC modeling of FLIP data provides physical parameters, this method will be of high value for quantitative comparison of protein aggregates in Huntington disease with that in other polyQ diseases, like various forms of ataxia. In fact, compressed exponential FL, similar as we found for eGFP-mtHtt has been reported in FLIP-experiments of ataxin-3 aggregates, in the nucleoplasm of COS7 cells [58
]. We are aware of the fact, that the presented two modelling approaches for FLIP data analysis are based on somehow contradictive assumptions: pixel-wise fitting reveals local heterogeneity of protein transport in various cellular pools, while MC modelling of FLIP experiments requires the assumption of well-mixed compartments. Solving this contradiction satisfactorily would require modelling the whole spatiotemporal protein dynamics including cell geometry, space-dependent diffusion constants, diffusion barriers, moving entities etc., but this is too ambitious at the moment and outside the scope of this article. We found that deviation of FL kinetics from a mono-exponential decay becomes negligible when larger cytoplasmic regions (above ~5 pixels) are included in the analysis (not shown). We also implemented a StrExp decay model for the FL in the bleached compartment (C2
) in our MC model, but that recovered a mono-exponential decay with h
= 1 (not shown, but see Figure C, green symbols and line). Together, with the observed time hierarchy, this makes the assumption of a well-mixed cytoplasmic compartment compared to measured FL of eGFP-Q73 in IB’s reasonable.