Abstract
We introduce a new, to our knowledge, numerical model based on spectral methods for analysis of fluorescence recovery after photobleaching data. The model covers pure diffusion and diffusion and binding (reaction-diffusion) with immobile binding sites, as well as arbitrary bleach region shapes. Fitting of the model is supported using both conventional recovery-curve-based estimation and pixel-based estimation, in which all individual pixels in the data are utilized. The model explicitly accounts for multiple bleach frames, diffusion (and binding) during bleaching, and bleaching during imaging. To our knowledge, no other fluorescence recovery after photobleaching framework incorporates all these model features and estimation methods. We thoroughly validate the model by comparison to stochastic simulations of particle dynamics and find it to be highly accurate. We perform simulation studies to compare recovery-curve-based estimation and pixel-based estimation in realistic settings and show that pixel-based estimation is the better method for parameter estimation as well as for distinguishing pure diffusion from diffusion and binding. We show that accounting for multiple bleach frames is important and that the effect of neglecting this is qualitatively different for the two estimation methods. We perform a simple experimental validation showing that pixel-based estimation provides better agreement with literature values than recovery-curve-based estimation and that accounting for multiple bleach frames improves the result. Further, the software developed in this work is freely available online.
Highlights
Diffusive transport properties in complex, soft matter fluctuate spatially and temporally and depend strongly on the degree of heterogeneity, obstruction effects, structural dynamics, and interactions with a matrix, e.g., binding effects [1]
We introduce a new, to our knowledge, numerical model based on spectral methods for analysis of fluorescence recovery after photobleaching (FRAP) data
Rate constants kon and koff will vary from 0.05 to 5 sÀ1; the rationale is that the timescales covered by the data ranges from Dt 1⁄4 0.2 s to 100Dt 1⁄4 20 s (50Dt 1⁄4 10 s in some cases), and the reciprocals of these values, i.e., 5 and 0.05 sÀ1, give an indication as to the range in which rate constants should be estimable using these data. These ranges for D, kon, and koff are further selected because they cover the typical range of values we have observed in soft materials, e.g., in gels [13]; other systems, e.g., cells, will result in different typical parameter ranges and in different experimental settings to begin with, such as pixel size and bleach region size
Summary
Diffusive transport properties in complex, soft matter fluctuate spatially and temporally and depend strongly on the degree of heterogeneity, obstruction effects, structural dynamics, and interactions with a matrix, e.g., binding effects [1]. Different approaches to FRAP for quantifying diffusion and binding interactions have shed light on how proteins interact with binding sites within the cell and nucleus [4,5,6], the transcription factor mobility in the nucleus [7] and its interaction with chromatin [8,9], interactions of membrane-associated proteins [10,11,12], and. Unbleached particles will move into the bleach region at a rate governed by the mobility and interaction parameters. This leads to a recovery of fluorescence in the bleach region. The physical/mathematical assumptions of the FRAP models as well as how the fitting is performed vary greatly between different approaches but boil down to representing the solution to a (reaction-)diffusion equation for the fluorescent species, analytically or numerically. We give a brief account of the literature for the factors that matter for the work below but refer the reader to the review in [2] for a more detailed account
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