In most biological processes, diffusion plays a critical role in transferring various bio-molecules to transfer desirable locations in an effective and energy-efficient manner. How fast molecules are ...transferred is measured by diffusion coefficients. Since each bio-molecules, in particular, signaling molecules have their unique diffusion coefficients and quantifying the diffusion coefficients help us to understand various time scales of both physiological and pathological processes in biological systems. Moreover, since diffusion profiles of a diffusant vary in different micro-environments of cell membranes, accurate diffusion coefficient also can provide a good picture of membrane landscapes as well as interactions of different membrane constituents. Currently, only a few experimental methods are available to assess the diffusion coefficient of a biomolecule of interest in live cells including Fluorescence Recovery After Photobleaching (FRAP). FRAP was developed to study diffusion processes of biomolecules in the cell membranes in the 1970s. Albeit its long history, the main principle of FRAP analysis has remained unchanged since its inception: fitting FRAP data to a theoretical diffusion model for the best fitting diffusion coefficient or using the relation between the half time of recovery and ROI size. In this study, we developed a flexible yet versatile confocal FRAP data analysis framework based on linear regression analysis which allows FRAP users to determine the diffusion from either single or multiple FRAP data points without data fitting. We also validated this approach for a series of fluorescently labeled soluble and membrane-bound proteins and lipids.
Quantitative measurements of diffusion can provide important information about how proteins and lipids interact with their environment within the cell and the effective size of the diffusing species. ...Confocal fluorescence recovery after photobleaching (FRAP) is one of the most widely accessible approaches to measure protein and lipid diffusion in living cells. However, straightforward approaches to quantify confocal FRAP measurements in terms of absolute diffusion coefficients are currently lacking. Here, we report a simplified equation that can be used to extract diffusion coefficients from confocal FRAP data using the half time of recovery and effective bleach radius for a circular bleach region, and validate this equation for a series of fluorescently labeled soluble and membrane‐bound proteins and lipids. We show that using this approach, diffusion coefficients ranging over three orders of magnitude can be obtained from confocal FRAP measurements performed under standard imaging conditions, highlighting its broad applicability.
The plasma membrane of mammalian cells is involved in a wide variety of cellular processes, including, but not limited to, endocytosis and exocytosis, adhesion and migration, and signaling. The ...regulation of these processes requires the plasma membrane to be highly organized and dynamic. Much of the plasma membrane organization exists at temporal and spatial scales that cannot be directly observed with fluorescence microscopy. Therefore, approaches that report on the membrane's physical parameters must often be utilized to infer membrane organization. As discussed here, diffusion measurements are one such approach that has allowed researchers to understand the subresolution organization of the plasma membrane. Fluorescence recovery after photobleaching (or FRAP) is the most widely accessible method for measuring diffusion in a living cell and has proven to be a powerful tool in cell biology research. Here, we discuss the theoretical underpinnings that allow diffusion measurements to be used in elucidating the organization of the plasma membrane. We also discuss the basic FRAP methodology and the mathematical approaches for deriving quantitative measurements from FRAP recovery curves. FRAP is one of many methods used to measure diffusion in live cell membranes; thus, we compare FRAP with two other popular methods: fluorescence correlation microscopy and single-particle tracking. Lastly, we discuss various plasma membrane organization models developed and tested using diffusion measurements.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Diffusion of proteins and lipids in lipid membranes plays a pivotal role in almost all aspects of cellular biology, including motility, exo−/endocytosis and signal transduction. For this reason, ...gaining a detailed understanding of membrane structure and function has long been a major area of cell biology research. To better elucidate this structure‐function relationship, various tools have been developed for diffusion measurements, including Fluorescence Recovery After Photobleaching (FRAP). Because of the complexity of cellular microenvironments, biological diffusion is often correlated over time and described by a time‐dependent diffusion coefficient,
D(t), although the underlying mechanisms are not fully understood. Since
D(t) provides important information regarding cellular structures, such as the existence of subresolution barriers to diffusion, many efforts have been made to quantify
D(t) by FRAP assuming a single power law,
D(t) = Γt
α − 1 where
Γ and
α are transport coefficient and anomalous exponent. However, straightforward approaches to quantify a general form of
D(t) are lacking. In this study, we develop a novel mathematical and computational framework to compute the mean square displacement of diffusing molecules and diffusion coefficient
D(t) from each individual time point of confocal FRAP data without the single power law assumption. Additionally, we developed an auxiliary equation for
D(t) which can readily distinguish normal diffusion or single power law anomalous diffusion from other types of anomalous diffusion directly from FRAP data. Importantly, by applying this approach to FRAP data from a variety of membrane markers, we demonstrate the single power law anomalous diffusion assumption is not sufficient to describe various types of
D(t) of membrane proteins. Lastly, we discuss how our new approaches can be applied to other fluorescence microscopy tools such as Fluorescence Correlation Spectroscopy (FCS) and Single Particle Tracking (SPT).
Although various evidence suggests the anomalous diffusion of membrane proteins, quantifying anomalous diffusion is still challenging even with technological advances in recent years. In this study, we develop a novel theoretical and computational framework to calculate time‐dependent diffusion coefficients (
D(t)) from individual FRAP data point and measure
D(t) of several membrane proteins to show that distinct types of anomalous diffusion exist in cell membranes.
Since its introduction in the 1970s, Fluorescence Correlation Spectroscopy (FCS) has become a standard biophysical and physical chemistry tool to investigate not only a diffusion but also a broad ...range of biochemical processes including binding kinetics and anomalous diffusion. Since the derivation of FCS equations for many biochemical processes shares many common steps with the diffusion FCS equation, it is important to understand the mathematical theory behind the diffusion FCS equation. However, because the derivation of FCS equations requires advanced Fourier Transform and inverse Fourier Transform theory, which most biologists and biochemists are not familiar with, it is often treated as a black box in practice. In this study, we provide a simple and straightforward step-by-step derivation of FCS equations for free diffusion based on calculus-level mathematics, so that FCS equations and its applications can be accessible to a broad audience. Additionally, we compare our derivation with the conventional Fourier Transform and inverse Fourier Transform theory based approach.
Since the introduction by Kermack and McKendrick in 1927, the Susceptible–Infected–Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious ...diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious diseases including recent COVID-19 breakouts, which stimulates the advance in mathematical epidemiology theory significantly. Some of the mathematical ideas and techniques developed are also relevant to motivate teaching various topics in differential equations by connecting students' life experiences with current pandemics to meaningful classroom learning activities. Here, various pedagogically relevant topics from the SIR model are provided for undergraduate differential equation class, which includes (1) compartmental modelling and mass action kinetic modelling, (2) conservation rule and model reduction, (3) introduction to phase plane by removing time variable to derive trajectory equations, (4) transformation of equations to equivalent forms, (5) transformation of second-order system to second-order ODE, (6) deriving an analytic solution to the SIR equation by solving Bernoulli's equation, (7) deriving an analytic solution to the SIR equation from trajectory equations and (8) deriving an analytic solution to the SIR equation from exponential substitutions.
Fluorescence Recovery After Photobleaching (FRAP) has been a versatile tool to study transport and reaction kinetics in live cells. Since the fluorescence data generated by fluorescence microscopy ...are in a relative scale, a wide variety of scalings and normalizations are used in quantitative FRAP analysis. Scaling and normalization are often required to account for inherent properties of diffusing biomolecules of interest or photochemical properties of the fluorescent tag such as mobile fraction or photofading during image acquisition. In some cases, scaling and normalization are also used for computational simplicity. However, to our best knowledge, the validity of those various forms of scaling and normalization has not been studied in a rigorous manner. In this study, we investigate the validity of various scalings and normalizations that have appeared in the literature to calculate mobile fractions and correct for photofading and assess their consistency with FRAP equations. As a test case, we consider linear or affine scaling of normal or anomalous diffusion FRAP equations in combination with scaling for immobile fractions. We also consider exponential scaling of either FRAP equations or FRAP data to correct for photofading. Using a combination of theoretical and experimental approaches, we show that compatible scaling schemes should be applied in the correct sequential order; otherwise, erroneous results may be obtained. We propose a hierarchical workflow to carry out FRAP data analysis and discuss the broader implications of our findings for FRAP data analysis using a variety of kinetic models.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The glycosphingolipid GM1 binds cholera toxin (CT) on host cells and carries it retrograde from the plasma membrane (PM) through endosomes, the trans-Golgi (TGN), and the endoplasmic reticulum (ER) ...to induce toxicity. To elucidate how a membrane lipid can specify trafficking in these pathways, we synthesized GM1 isoforms with alternate ceramide domains and imaged their trafficking in live cells. Only GM1 with unsaturated acyl chains sorted efficiently from PM to TGN and ER. Toxin binding, which effectively crosslinks GM1 lipids, was dispensable, but membrane cholesterol and the lipid raft-associated proteins actin and flotillin were required. The results implicate a protein-dependent mechanism of lipid sorting by ceramide structure and provide a molecular explanation for the diversity and specificity of retrograde trafficking by CT in host cells.
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► Cells sort the glycosphingolipid GM1 by the structure of its ceramide domain (76/89) ► Only unsaturated GM1 ceramides sort retrograde all the way to the ER (64/78) ► GM1 is the vehicle that carries cholera toxin from plasma membrane to ER (61/74) ► Flotillin, cholesterol, and actin are required for GM1 sorting (55/64)
Chinnapen et al. examine how membrane lipids are sorted in mammalian cells and how the membrane glycosphingolipid GM1 can direct cholera toxin trafficking from cell surface into the ER of host cells to cause disease. Their results implicate a protein-dependent mechanism of sorting GM1, determined by its unsaturated ceramide domain.
The process of autophagy involves the formation of autophagosomes, double-membrane structures that encapsulate cytosol. Microtubule-associated protein light chain 3 (LC3) was the first protein shown ...to specifically label autophagosomal membranes in mammalian cells, and subsequently EGFP-LC3 has become one of the most widely utilized reporters of autophagy. Although LC3 is currently thought to function primarily in the cytosol, the site of autophagosome formation, EGFP-LC3 often appears to be enriched in the nucleoplasm relative to the cytoplasm in published fluorescence images. However, the nuclear pool of EGFP-LC3 has not been specifically studied in previous reports, and mechanisms by which LC3 shuttles between the cytoplasm and nucleoplasm are currently unknown. In this study, we therefore investigated the regulation of the nucleo-cytoplasmic distribution of EGFP-LC3 in living cells. By quantitative fluorescence microscopy analysis, we demonstrate that soluble EGFP-LC3 is indeed enriched in the nucleus relative to the cytoplasm in two commonly studied cell lines, COS-7 and HeLa. Although LC3 contains a putative nuclear export signal (NES), inhibition of active nuclear export or mutation of the NES had no effect on the nucleo-cytoplasmic distribution of EGFP-LC3. Furthermore, FRAP analysis indicates that EGFP-LC3 undergoes limited passive nucleo-cytoplasmic transport under steady state conditions, and that the diffusional mobility of EGFP-LC3 was substantially slower in the nucleus and cytoplasm than predicted for a freely diffusing monomer. Induction of autophagy led to a visible decrease in levels of soluble EGFP-LC3 relative to autophagosome-bound protein, but had only modest effects on the nucleo-cytoplasmic ratio or diffusional mobility of the remaining soluble pools of EGFP-LC3. We conclude that the enrichment of soluble EGFP-LC3 in the nucleus is maintained independently of active nuclear export or induction of autophagy. Instead, incorporation of soluble EGFP-LC3 into large macromolecular complexes within both the cytoplasm and nucleus may prevent its rapid equilibrium between the two compartments.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
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