Anomalous Diffusion Characterization by Fourier Transform-FRAP with Patterned Illumination

Abstract

Fourier transform fluorescence recovery after photobleaching (FT-FRAP) with patterned illumination is theorized and demonstrated for quantitatively evaluating normal and anomalous diffusion. Diffusion characterization is routinely performed to assess mobility in cell biology, pharmacology, and food science. Conventional FRAP is noninvasive, has low sample volume requirements, and can rapidly measure diffusion over distances of a few micrometers. However, conventional point-bleach measurements are complicated by signal-to-noise limitations, the need for precise knowledge of the bleach beam profile, potential for bias due to sample heterogeneity, and poor compatibility with multi-photon excitation due to local heating. In FT-FRAP with patterned illumination, the time-dependent fluorescence recovery signal is concentrated to puncta in the spatial Fourier domain through patterned bleaching, with substantial improvements in signal-to-noise, mathematical simplicity, representative sampling, and multiphoton compatibility. A custom nonlinear-optical beam-scanning microscope enabled patterned illumination for photobleaching through two-photon excitation. Measurements in the spatial Fourier domain removed dependence on the bleach profile, suppressing bias from imprecise knowledge of the point spread function. For normal diffusion, the fluorescence recovery produced a simple single-exponential decay in the spatial Fourier domain, in excellent agreement with theoretical predictions. Simultaneous measurement of diffusion at multiple length scales was enabled through analysis of multiple spatial harmonics of the bleaching pattern. Anomalous diffusion was characterized by FT-FRAP through a nonlinear fit to multiple spatial harmonics of the fluorescence recovery. Constraining the fit to describe diffusion over multiple length scales resulted in higher confidence in the recovered fitting parameters. Additionally, phase analysis in FT-FRAP was shown to inform on flow/sample translation. Statement of SignificanceFourier transform fluorescence recovery after photobleaching (FT-FRAP) with patterned illumination greatly improves the accuracy of diffusion assessments and simultaneously accesses information on both normal and anomalous diffusion in a single experiment..

Analysis of chemical and mechanical behaviors in living cells by continuum mechanics-based FRAP

“…Numerous FRAP methods have been proposed to evaluate the complex turnover in a normal diffusion-driven case (8)(9)(10)(11)(12), anomalous diffusion-driven case (13)(14)(15)(16), chemical reactiondriven case (4, 5), and diffusion-reaction case (4,7,17). However, because of the current lack of appropriate FRAP methods, the "long-term" turnover driven by stress fiber-associated active dynamics that include both intracellular bulk-like flow and microscopic structural deformation remains highly elusive.…”

“…The diffusion coefficient is then pragmatically estimated by considering the size of the bleached region and the time constant (8) or more accurately by analyzing the spatiotemporal fluorescence profile with a diffusion equation instead of single exponential functions (9)(10)(11)(12). For more complicated cases with anomalous diffusion, fractional diffusion equation (13), alternative point FRAP (14), computational framework (15), and Fourier transform-FRAP with patterned photobleaching (16) have been developed to evaluate the effect of intracellular molecular crowding. Moreover, in a mixed case where diffusive molecules associate and dissociate with their reaction partners, mathematical models considering reaction-diffusion equations (4,17,18), FRAP combined with fluorescence correlation spectroscopy (19), and FRAP combined with genetic manipulation (7) have been developed to separately determine the diffusion coefficient and binding kinetics.…”

Fluorescence-Detected Mid-Infrared Photothermal Microscopy

“…35 Comparisons of Figure 4B and 4D indicate clear structural similarities between the phaseseparated domains corresponding to ritonavir as identified by F-PTIR spectroscopy with those producing native TPE-UVF in the absence of a fluorescent marker. Spatial Fourier transform fluorescence recovery after photobleaching experiments (FT-FRAP) following Geiger et al 36 confirm fluidity within the two phase-separated domains, with ∼3-fold lower viscosity within the brightly fluorescent domains (see Supporting Information for details).…”

“…Spatial Fourier transform fluorescence recovery after photobleaching experiments (FT-FRAP) following Geiger et al confirm fluidity within the two phase-separated domains, with ∼3-fold lower viscosity within the brightly fluorescent domains (see Supporting Information for details).…”

A noninvasive fluorescence imaging-based platform measures 3D anisotropic extracellular diffusion

“…The ability of LiFT-FRAP to discriminate between different models of diffusion, such as anomalous diffusion, was not explored in this study. However, given the successful demonstration of the spatial Fourier analysis method for simultaneous measurement of both normal diffusion and binding rate in 2D 64 , 65 , our method could be extended to quantify more complex 3D diffusion behaviors in the future.…”