Analysis of Active Transport by Fluorescence Recovery after Photobleaching

Abstract

Fluorescence recovery after photobleaching (FRAP) is a well-established experimental technique to study binding and diffusion of molecules in cells. Although a large number of analytical and numerical models have been developed to extract binding and diffusion rates from FRAP recovery curves, active transport of molecules is typically not included in the existing models that are used to estimate these rates. Here we present a validated numerical method for estimating diffusion, binding/unbinding rates, and active transport velocities using FRAP data that captures intracellular dynamics through partial differential equation models. We apply these methods to transport and localization of mRNA molecules in Xenopus laevis oocytes, where active transport processes are essential to generate developmental polarity. By providing estimates of the effective velocities and diffusion, as well as expected run times and lengths, this approach can help quantify dynamical properties of localizing and nonlocalizing RNA. Our results confirm the distinct transport dynamics in different regions of the cytoplasm, and suggest that RNA movement in both the animal and vegetal directions may influence the timescale of RNA localization in Xenopus oocytes. We also show that model initial conditions extracted from FRAP postbleach intensities prevent underestimation of diffusion, which can arise from the instantaneous bleaching assumption. The numerical and modeling approach presented here to estimate parameters using FRAP recovery data is a broadly applicable tool for systems where intracellular transport is a key molecular mechanism.

From continuous-time random walks to controlled-diffusion reaction

“…defines a uniform reaction process in space and was extensively investigated in literature [56][57][58][59][60][61]. Here, we propose that a reaction process between two species occurs in a specific point which defines a controlled-reaction for two species.…”

Modeling Microtubule-Based Transport and Anchoring of mRNA

“…mRNA cargoes (red) are transported by motor proteins (black) along polarized microtubule filaments (blue lines) towards the vegetal cortex. The vegetal cytoplasm is schematically divided into three regions where transport parameters have been found to differ [10].…”

“…In our previous work [10] (see also [41]), we used linear transport models coupled with parameter estimation and analysis to determine diffusion coefficients, motor speeds, and switching rates for the transitions on and off microtubules for dynamic populations of mRNA in Xenopus oocytes using FRAP (fluorescence recovery after photobleaching) data [17]. The analysis there allowed us to suggest differences in transport efficiency of mRNA in different regions of the oocyte cytoplasm.…”

“…These constant transition rate models are useful in modeling dynamics on the short timescale of the FRAP experiments; however, they cannot provide insights onto the longer timescale of mRNA localization, where the transport directionality depends on the complex microtubule cytoskeleton. Here we build on the models and parameter estimates in [10] and incorporate the spatial microtubule networks through spatially dependent transition rates. We carry out a large-time analysis of reaction-advection-diffusion transport models on parallel filaments using Fourier expansion and Lyapunov-Schmidt reduction and extend existing effective transport results [8] to general systems with an arbitrary number of dynamical states and under no assumptions on the scales of the parameters or on the filament density.…”

“…The models we propose do not explicitly account for the polarity (plus/minus ends) of the microtubules or for the specific motor species carrying out the transport in each region. Instead, we assume that this information is embedded in the different kinetic parameters estimated for each region of the Xenopus oocyte cytoplasm (see Figure 1) in [10]. The models proposed do, however, account for the geometry and orientation of the microtubule filaments in the domain, which we henceforth refer to as the microtubule structure.…”