Analysis of Active Transport by Fluorescence Recovery after Photobleaching

Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching

Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that many established in vivo measurements of protein dynamics average out the spatial dimensions. Here, we are motivated by recent experiments on the binding dynamics of the RNA-binding protein PTBP3 in RNP granules of frog oocytes based on fluorescence recovery after photobleaching (FRAP) measurements. FRAP is a widely-used experimental technique for probing protein dynamics in living cells, and is often modeled using simple reaction-diffusion models of the protein dynamics. We show that current methods of structural and practical parameter identifiability provide limited insights into identifiability of kinetic parameters for these PDE models and spatially-averaged FRAP data. We thus propose a pipeline for assessing parameter identifiability and for learning parameter combinations based on re-parametrization and profile likelihoods analysis. We show that this method is able to recover parameter combinations for synthetic FRAP datasets and investigate its application to real experimental data.

Long-Term Fluorescence Recovery After Photobleaching (FRAP)

Numerous models have been developed for the analysis of fluorescence recovery after photobleaching (FRAP), by which intracellular diffusion and turnover rate are quantitatively evaluated. FRAP analyses typically focus on such events that occur within several minutes, but to precisely evaluate a slow turnover rate of particularly actin stress fibers, achieving long-term FRAP observations of more than 10 min is necessary. In such long-term observations, the effect of intracellular advection is no longer ignored, which motivated us to develop a novel method to decouple the multiple factors associated with the long FRAP response. This method allows us to distinguish the origin of mechanobiological responses of stress fibers that come from either the level of individual actin filaments or that of actin monomers.

Long-term molecular turnover of actin stress fibers revealed by advection-reaction analysis in fluorescence recovery after photobleaching

Fluorescence recovery after photobleaching (FRAP) is a versatile technique to evaluate the intracellular molecular exchange called turnover. Mechanochemical models of FRAP typically consider the molecular diffusion and chemical reaction that simultaneously occur on a time scale of seconds to minutes. Particularly for long-term measurements, however, a mechanical advection effect can no longer be ignored, which transports the proteins in specific directions within the cells and accordingly shifts the spatial distribution of the local chemical equilibrium. Nevertheless, existing FRAP models have not considered the spatial shift, and as such, the turnover rate is often analyzed without considering the spatiotemporally updated chemical equilibrium. Here we develop a new FRAP model aimed at long-term measurements to quantitatively determine the two distinct effects of the advection and chemical reaction, i.e., the different major sources of the change in fluorescence intensity. To validate this approach, we carried out FRAP experiments on actin in stress fibers over a time period of more than 900 s, and the advection rate was shown to be comparable in magnitude to the chemical dissociation rate. We further found that the actin–myosin interaction and actin polymerization differently affect the advection and chemical dissociation. Our results suggest that the distinction between the two effects is indispensable to extract the intrinsic chemical properties of the actin cytoskeleton from the observations of complicated turnover in cells.

Using Fluorescence Recovery After Photobleaching data to uncover filament dynamics

Fluorescence Recovery After Photobleaching (FRAP) has been extensively used to understand molecular dynamics in cells. This technique when applied to soluble, globular molecules driven by diffusion is easily interpreted and well understood. However, the classical methods of analysis cannot be applied to anisotropic structures subjected to directed transport, such as cytoskeletal filaments or elongated organelles transported along microtubule tracks. A new mathematical approach is needed to analyze FRAP data in this context and determine what information can be obtain from such experiments. To address these questions, we analyze fluorescence intensity profile curves after photobleaching of fluorescently labelled intermediate filaments anterogradely transported along microtubules. We apply the analysis to intermediate filament data to determine information about the filament motion. Our analysis consists of deriving equations for fluorescence intensity profiles and developing a mathematical model for the motion of filaments and simulating the model. Two closed forms for profile curves were derived, one for filaments of constant length and one for filaments with constant velocity, and three types of simulation were carried out. In the first type of simulation, the filaments have random velocities which are constant for the duration of the simulation. In the second type, filaments have random velocities which instantaneously change at random times. In the third type, filaments have random velocities and exhibit pausing between velocity changes. Our analysis shows: the most important distribution governing the shape of the intensity profile curves obtained from filaments is the distribution of the filament velocity. Furthermore, filament length which is constant during the experiment, had little impact on intensity profile curves. Finally, gamma distributions for the filament velocity with pauses give the best fit to asymmetric fluorescence intensity profiles of intermediate filaments observed in FRAP experiments performed in polarized migrating astrocytes. Our analysis also shows that the majority of filaments are stationary. Overall, our data give new insight into the regulation of intermediate filament dynamics during cell migration.

Fluorescence Recovery After Photobleaching (FRAP) is a commonly-used technique to analyze the dynamics of fluorescently-tagged proteins or structures in biology. After photochemical altering the fluorophor in a specific region, fluorescent material from the surrounding region moves into the photobleached region. Usually applied to the diffusion of soluble or membrane associate proteins, the existing models of analysis are not suitable for the elucidation of directional transport of elongated structures. Different modes of motions for the elongated structures with distributed lengths and velocities in cells are considered. First, we observe that filament lengths can be inferred from the level of noisiness. We further show the characteristics of fluorescence profile curves mainly depend on the occurrence of changes in velocities and distributions of velocities; whereas length distributions have negligible impact. Analysis of experimental data using this new framework indicates intermediate filaments transported by kinesins along microtubules in polarized migrating cells have gamma distributed velocities changing over time between pausing. Most filaments are found to be very slow or stationary with a few moving fast. This new computational approach should permit the interpretation of FRAP experimental data obtained with any directionally moving elongated structures of various lengths.

Analysis of chemomechanical behavior of stress fibers by continuum mechanics-based FRAP

Fluorescence recovery after photobleaching (FRAP) is a common technique to analyze the turnover of molecules in living cells. Numerous physicochemical models have been developed to quantitatively evaluate the rate of turnover driven by chemical reaction and diffusion that occurs in a few seconds to minutes. On the other hand, they have limitations in interpreting long-term FRAP responses where intracellular active movement inevitably provides target molecular architectures with additional effects other than chemical reaction and diffusion, namely directed transport and structural deformation. To overcome the limitations, we develop a continuum mechanics-based model that allows for decoupling FRAP response into the intrinsic turnover rate and subcellular mechanical characteristics such as displacement vector and strain tensor. Our approach was validated using fluorescently labeled β-actin in an actomyosin-mediated contractile apparatus called stress fibers, revealing spatially distinct patterns of the multi-physicochemical events, in which the turnover rate, which represents effective off-rate of β-actin, was significantly higher at the center of the cell. We also found that the turnover rate is negatively correlated with the rate of displacement or velocity along stress fibers but, interestingly, not with the absolute magnitude of strain. Moreover, stress fibers are subjected to centripetal flow that is facilitated by the circulation of actin molecules. Taken together, this novel framework for long-term FRAP analysis allows for unveiling the contribution of overlooked microscopic mechanics to molecular turnover in living cells.

Molecular and cellular cues governing nanomaterial-mucosae interactions: from nanomedicine to nanotoxicology

Mucosal tissues constitute the largest interface between the body and the surrounding environment and they regulate the access of molecules, supramolecular structures, particulate matter, and pathogens into it. All mucosae are characterized by an outer mucus layer that protects the underlying cells from physicochemical, biological and mechanical insults, a mono-layered or stratified epithelium that forms tight junctions and controls the selective transport of solutes across it and associated lymphoid tissues that play a sentinel role. Mucus is a gel-like material comprised mainly of the glycoprotein mucin and water and it displays both hydrophilic and hydrophobic domains, a net negative charge, and high porosity and pore interconnectivity, providing an efficient barrier for the absorption of therapeutic agents. To prolong the residence time, absorption and bioavailability of a broad spectrum of active compounds upon mucosal administration, mucus-penetrating and mucoadhesive particles have been designed by tuning the chemical composition, the size, the density, and the surface properties. The benefits of utilizing nanomaterials that interact intimately with mucosae by different mechanisms in the nanomedicine field have been extensively reported. To ensure the safety of these nanosystems, their compatibility is evaluated in vitro and in vivo in preclinical and clinical trials. Conversely, there is a growing concern about the toxicity of nanomaterials dispersed in air and water effluents that unintentionally come into contact with the airways and the gastrointestinal tract. Thus, deep understanding of the key nanomaterial properties that govern the interplay with mucus and tissues is crucial for the rational design of more efficient drug delivery nanosystems (nanomedicine) and to anticipate the fate and side-effects of nanoparticulate matter upon acute or chronic exposure (nanotoxicology). This review initially overviews the complex structural features of mucosal tissues, including the structure of mucus, the epithelial barrier, the mucosal-associated lymphatic tissues and microbiota. Then, the most relevant investigations attempting to identify and validate the key particle features that govern nanomaterial-mucosa interactions and that are relevant in both nanomedicine and nanotoxicology are discussed in a holistic manner. Finally, the most popular experimental techniques and the incipient use of mathematical and computational models to characterize these interactions are described.

Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport

In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion dynamics is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed renewal reward framework are illustrated for several case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of molecular motor proteins.

Testing Models of mRNA Localization Reveals Robustness Regulated by Reducing Transport between Cells

Robust control of gene expression in both space and time is of central importance in the regulation of cellular processes and for multicellular development. However, the mechanisms by which robustness is achieved are generally not identified or well understood. For example, messenger RNA (mRNA) localization by molecular motor-driven transport is crucial for cell polarization in numerous contexts, but the regulatory mechanisms that enable this process to take place in the face of noise or significant perturbations are not fully understood. Here, we use a combined experimental-theoretical approach to characterize the robustness of gurken/transforming growth factor-α mRNA localization in Drosophila egg chambers, where the oocyte and 15 surrounding nurse cells are connected in a stereotypic network via intracellular bridges known as ring canals. We construct a mathematical model that encodes simplified descriptions of the range of steps involved in mRNA localization, including production and transport between and within cells until the final destination in the oocyte. Using Bayesian inference, we calibrate this model using quantitative single molecule fluorescence in situ hybridization data. By analyzing both the steady state and dynamic behaviors of the model, we provide estimates for the rates of different steps of the localization process as well as the extent of directional bias in transport through the ring canals. The model predicts that mRNA synthesis and transport must be tightly balanced to maintain robustness, a prediction that we tested experimentally using an overexpression mutant. Surprisingly, the overexpression mutant fails to display the anticipated degree of overaccumulation of mRNA in the oocyte predicted by the model. Through careful model-based analysis of quantitative data from the overexpression mutant, we show evidence of saturation of the transport of mRNA through ring canals. We conclude that this saturation engenders robustness of the localization process in the face of significant variation in the levels of mRNA synthesis.

Modeling microtubule-based transport and anchoring of mRNA

Localization of messenger RNA (mRNA) at the vegetal cortex plays an important role in the early development of Xenopus laevis oocytes. While it is known that molecular motors are responsible for the transport of mRNA cargo along microtubules to the cortex, the mechanisms of localization remain unclear. We model cargo transport along microtubules using partial differential equations with spatially-dependent rates. A theoretical analysis of reduced versions of our model predicts effective velocity and diffusion rates for the cargo and shows that randomness of microtubule networks enhances effective transport. A more complex model using parameters estimated from fluorescence microscopy data reproduces the spatial and timescales of mRNA localization observed in Xenopus oocytes, corroborates experimental hypotheses that anchoring may be necessary to achieve complete localization, and shows that anchoring of mRNA complexes actively transported to the cortex is most effective in achieving robust accumulation at the cortex.

Fluorescence techniques in developmental biology

Advanced fluorescence techniques, commonly known as the F-techniques, measure the kinetics and the interactions of biomolecules with high sensitivity and spatiotemporal resolution. Applications of the F-techniques, which were initially limited to cells, were further extended to study in vivo protein organization and dynamics in whole organisms. The integration of F-techniques with multi-photon microscopy and light-sheet microscopy widened their applications in the field of developmental biology. It became possible to penetrate the thick tissues of living organisms and obtain good signal-to-noise ratio with reduced photo-induced toxicity. In this review, we discuss the principle and the applications of the three most commonly used F-techniques in developmental biology: Fluorescence Recovery After Photo-bleaching (FRAP), Fo¨ rster Resonance Energy Transfer (FRET), and Fluorescence Correlation and Cross-Correlation Spectroscopy (FCS and FCCS).