Methods for measuring rates of protein binding to insoluble scaffolds in living cells: histone H1-chromatin interactions

Understanding of cell regulation is limited by our inability to measure molecular binding rates for proteins within the structural context of living cells, and many systems biology models are hindered because they use values obtained with molecules binding in solution. Here, we present a kinetic analysis of GFP-histone H1 binding to chromatin within nuclei of living cells that allows both the binding rate constant k(ON) and dissociation rate constant k(OFF) to be determined based on data obtained from fluorescence recovery after photobleaching (FRAP) analysis. This is accomplished by measuring the ratio of bound to free concentration of protein at steady state, and identifying the rate-determining step during FRAP recovery experimentally, combined with mathematical modeling. We report k(OFF) = 0.0131/s and k(ON) = 0.14/s for histone H1.1 binding to chromatin. This work brings clarity to the interpretation of FRAP experiments and provides a way to determine binding kinetics for nuclear proteins and other cellular molecules that interact with insoluble scaffolds within living cells.     

Using FRAP and mathematical modeling to determine the in vivo kinetics of nuclear proteins

Fluorescence recovery after photobleaching (FRAP) has become a popular technique to investigate the behavior of proteins in living cells. Although the technique is relatively old, its application to studying endogenous intracellular proteins in living cells is relatively recent and is a consequence of the newly developed fluorescent protein-based living cell protein tags. This is particularly true for nuclear proteins, in which endogenous protein mobility has only recently been studied. Here we examine the experimental design and analysis of FRAP experiments. Mathematical modeling of FRAP data enables the experimentalist to extract information such as the association and dissociation constants, distribution of a protein between mobile and immobilized pools, and the effective diffusion coefficient of the molecule under study. As experimentalists begin to dissect the relative influence of protein domains within individual proteins, this approach will allow a quantitative assessment of the relative influences of different molecular interactions on the steady-state distribution and protein function in vivo.     

Investigation of binding mechanisms of nuclear proteins using confocal scanning laser microscopy and FRAP

Fluorescence recovery after photobleaching (FRAP) measurements offer an important tool towards analysing diffusion processes within living biological cells. A model is presented that aims to provide a rigorous theoretical framework from which binding information of proteins from FRAP data can be extracted. A single binding reaction is considered and a set of mathematical equations is introduced that incorporates the concentration of free proteins, vacant binding sites and bound complexes in addition to the on- and off-rates of the proteins. To allow a realistic FRAP model, characteristics of the instruments used to perform FRAP measurements are included in the equation. The proposed model has been designed to be applied to biological samples with a confocal scanning laser microscope (CSLM) equipped with the feature to bleach regions characterised by a radially Gaussian distributed profile. Binding information emerges from FRAP simulations considering the diffusion coefficient, radial extent of the bleached volume and bleach constant as parameters derived from experimental data. The proposed model leads to FRAP curves that depend on the on- and off-rates. Analytical expressions are used to define the boundaries of on- and off-rate parameter space in simplified cases when molecules can move on an infinite domain. A similar approach is ensued when movement is restricted in a compartment with a finite size. The theoretical model can be used in conjunction to experimental data acquired by CSLM to investigate the biophysical properties of proteins in living cells.     

Intracellular macromolecular mobility measured by fluorescence recovery after photobleaching with confocal laser scanning microscopes

Fluorescence recovery after photobleaching (FRAP) is a widely used tool for estimating mobility parameters of fluorescently tagged molecules in cells. Despite the widespread use of confocal laser scanning microscopes (CLSMs) to perform photobleaching experiments, quantitative data analysis has been limited by lack of appropriate practical models. Here, we present a new approximate FRAP model for use on any standard CLSM. The main novelty of the method is that it takes into account diffusion of highly mobile molecules during the bleach phase. In fact, we show that by the time the first postbleach image is acquired in a CLSM a significant fluorescence recovery of fast-moving molecules has already taken place. The model was tested by generating simulated FRAP recovery curves for a wide range of diffusion coefficients and immobile fractions. The method was further validated by an experimental determination of the diffusion coefficient of fluorescent dextrans and green fluorescent protein. The new FRAP method was used to compare the mobility rates of fluorescent dextrans of 20, 40, 70, and 500 kDa in aqueous solution and in the nucleus of living HeLa cells. Diffusion coefficients were lower in the nucleoplasm, particularly for higher molecular weight dextrans. This is most likely caused by a sterical hindrance effect imposed by nuclear components. Decreasing the temperature from 37 to 22 degrees C reduces the dextran diffusion rates by approximately 30% in aqueous solution but has little effect on mobility in the nucleoplasm. This suggests that spatial constraints to diffusion of dextrans inside the nucleus are insensitive to temperature.     

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.     

荧光漂白后恢复技术及其在活细胞分子机制研究中的应用

荧光漂白后恢复（FRAP）是一项利用荧光探针研究活体细胞中各类分子迁移特性的技术。简要介绍了FRAP技术的原理和具体实施要求,列出了动态比和扩散系数的计算公式,并例举了近几年FRAP技术在细胞分子机制研究中的应用。     

Line FRAP with the confocal laser scanning microscope for diffusion measurements in small regions of 3-D samples

We present a truly quantitative fluorescence recovery after photobleaching (FRAP) model for use with the confocal laser scanning microscope based on the photobleaching of a long line segment. The line FRAP method is developed to complement the disk FRAP method reported before. Although being more subject to the influence of noise, the line FRAP model has the advantage of a smaller bleach region, thus allowing for faster and more localized measurements of the diffusion coefficient and mobile fraction. The line FRAP model is also very well suited to examine directly the influence of the bleaching power on the effective bleaching resolution. We present the outline of the mathematical derivation, leading to a final analytical expression to calculate the fluorescence recovery. We examine the influence of the confocal aperture and the bleaching power on the measured diffusion coefficient to find the optimal experimental conditions for the line FRAP method. This will be done for R-phycoerythrin and FITC-dextrans of various molecular weights. The ability of the line FRAP method to measure correctly absolute diffusion coefficients in three-dimensional samples will be evaluated as well. Finally we show the application of the method to the simultaneous measurement of free green fluorescent protein diffusion in the cytoplasm and nucleus of living A549 cells.     

A closed-form analytic expression for FRAP formula for the binding diffusion model

One of the most dominant methods cells use for a large class of cellular processes is reaction (or binding) diffusion kinetics, which are controlled by kinetic constants such as diffusion coefficients and on/off binding rate constants. Fluorescence recovery after photobleaching (FRAP) can be used to determine these kinetic constants in living cells. While an analytic expression for FRAP formulae for pure diffusion has been available for some time, an analytic FRAP formula for the binding diffusion model has not been reported yet. Here, we present an analytic FRAP formula for the binding diffusion model in an explicit form allowing for diffusion of the bound complex for either a uniform circle laser profile or a Gaussian laser profile.     

Expanding the scope of quantitative FRAP analysis

In this study, new mathematical models were developed for analysis of fluorescence recovery after photobleaching (FRAP) data to account for features not represented in previous analysis: conical photobleaching geometry, spatial variations in binding of fluorescent molecules, and directed transport of fluorescent molecules. To facilitate computations in conical geometry, a fast computational method for calculation of fluorescence recovery is presented. Two approximations are presented to aid in FRAP analysis when binding varies spatially, one applying to cases of relatively fast diffusion and slow binding and the other to binding of molecules to small cellular structures. Numerical results show that using a model that represents the influential physical processes and that is formulated in the appropriate geometry can substantially improve the accuracy of FRAP calculations.     

Mechanical forces alter zyxin unbinding kinetics within focal adhesions of living cells

The formation of focal adhesions that mediate alterations of cell shape and movement is controlled by a mechanochemical mechanism in which cytoskeletal tensional forces drive changes in molecular assembly; however, little is known about the molecular biophysical basis of this response. Here, we describe a method to measure the unbinding rate constant k(OFF) of individual GFP-labeled focal adhesion molecules in living cells by modifying the fluorescence recovery after photobleaching (FRAP) technique and combining it with mathematical modeling. Using this method, we show that decreasing cellular traction forces on focal adhesions by three different techniques--chemical inhibition of cytoskeletal tension generation, laser incision of an associated actin stress fiber, or use of compliant extracellular matrices--increases the k(OFF) of the focal adhesion protein zyxin. In contrast, the k(OFF) of another adhesion protein, vinculin, remains unchanged after tension dissipation. Mathematical models also demonstrate that these force-dependent increases in zyxin's k(OFF) that occur over seconds are sufficient to quantitatively predict large-scale focal adhesion disassembly that occurs physiologically over many minutes. These findings demonstrate that the molecular binding kinetics of some, but not all, focal adhesion proteins are sensitive to mechanical force, and suggest that force-dependent changes in this biophysical parameter may govern the supramolecular events that underlie focal adhesion remodeling in living cells.     

Behavior of a fluorescent analogue of calmodulin in living 3T3 cells

We have prepared and partially characterized a lissamine-rhodamine B fluorescent analogue of calmodulin, LRB-CM. The analogue had a dye/protein ratio of approximately 1.0 and contained no free dye or contaminating labeled proteins. LRB-CM was indistinguishable from native calmodulin upon SDS PAGE and in assays of phosphodiesterase and myosin light chain kinase. The emission spectrum of LRB-CM was insensitive to changes in pH, ionic strength, and temperature over the physiological range, but the apparent quantum yield was influenced somewhat by divalent cation concentration. LRB-CM injected into living Swiss 3T3 fibroblasts became associated with nitrobenzoxadiazole-phallacidin staining stress fibers in some interphase cells. LRB-CM and acetamidofluorescein-labeled actin co-injected into the same cell both became associated with fibers in some cells, but in most cases association of the two analogues with fibers was mutually exclusive. This suggests that calmodulin may differ from actin in the timing of incorporation into stress fibers or that we have distinguished distinct populations of stress fibers. We were able to detect no direct interaction of LRB-CM with actin by fluorescence photobleaching recovery (FRAP) of aqueous solutions. Interaction of LRB-CM with myosin light chain kinase also was not detected by FRAP. This suggests that the mean lifetime of the calmodulin-myosin light chain kinase complex is too short to affect the diffusion coefficient of calmodulin. We examined various fluorescent derivatives of proteins and dextrans as suitable control molecules for quantitative fluorescent analogue cytochemistry in living cells. Fluorescein isothiocyanate-dextrans were found to be preferable to all the proteins tested, since their mobilities in cytoplasm were inversely dependent on molecular size and there was no evidence of binding to intracellular components. In contrast, FRAP of LRB-CM in the cytoplasm of living 3T3 cells suggested that the analogue interacts with intracellular components with a range of affinities. The mobility of LRB-CM in the cytoplasm was sensitive to treatment of the cells with trifluoperazine, which suggests that at least some of the intracellular binding sites are specific for calmodulin in the calcium-bound form. FRAP of LRB-CM in the nuclei of living 3T3 cells indicated that the analogue was highly mobile within the nucleus but entered the nucleus from the cytoplasm much more slowly than fluorescein isothiocyanate-dextran of comparable molecular size and much more slowly than predicted from its mobility in cytoplasm.     

A reaction-diffusion model to study RNA motion by quantitative fluorescence recovery after photobleaching

Fluorescence recovery after photobleaching (FRAP) is a powerful technique to study molecular dynamics inside living cells. During the past years, several laboratories have used FRAP to image the motion of RNA-protein and other macromolecular complexes in the nucleus and cytoplasm. In the case of mRNAs, there is growing evidence indicating that these molecules assemble into large ribonucleoprotein complexes that diffuse throughout the nucleus by Brownian motion. However, estimates of the corresponding diffusion rate yielded values that differ by up to one order of magnitude. In vivo labeling of RNA relies on indirect tagging with a fluorescent probe, and here we show how the binding affinity of the probe to the target RNA influences the effective diffusion estimates of the resulting complex. We extend current reaction-diffusion models for FRAP by allowing for diffusion of the bound complex. This more general model can be used to fit any fluorescence recovery curve involving two interacting mobile species in the cell (a fluorescent probe and its target substrate). The results show that interpreting FRAP data in light of the new model reconciles the discrepant mRNA diffusion-rate values previously reported.     

A Generalization of Theory for Two-Dimensional Fluorescence Recovery after Photobleaching Applicable to Confocal Laser Scanning Microscopes

Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells.     

Investigating complexity of protein-protein interactions in focal adhesions

The formation of focal adhesions governs cell shape and function; however, there are few measurements of the binding kinetics of focal adhesion proteins in living cells. Here, we used the fluorescence recovery after photobleaching (FRAP) technique, combined with mathematical modeling and scaling analysis to quantify dissociation kinetics of focal adhesion proteins in capillary endothelial cells. Novel experimental protocols based on mathematical analysis were developed to discern the rate-limiting step during FRAP. Values for the dissociation rate constant k_OFF ranged over an order of magnitude from 0.009 ± 0.001/s for talin to 0.102 ± 0.010/s for FAK, indicating that talin is bound more strongly than other proteins in focal adhesions. Comparisons with in vitro measurements reveal that multiple focal adhesion proteins form a network of bonds, rather than binding in a pair-wise manner in these anchoring structures in living cells.     

Fluorescence correlation microscopy of cells in the presence of autofluorescence.

Fluorescence correlation microscopy (FCM), the combination of fluorescence correlation spectroscopy (FCS) and digital microscopy (Brock and Jovin, 1998. Cell. Mol. Biol. 44:847-856), has been implemented for measuring molecular diffusion and association in living cells with explicit consideration of autocorrelations arising from autofluorescence. Autofluorescence excited at 532 nm colocalizes with mitochondria, has flavin-like spectral characteristics, exhibits relaxation times characteristic for the diffusion of high-molecular-weight proteins, and depends on the incubation conditions of the cells. These time- and location-dependent properties preclude the assignment of universal background parameters. The lower limit for detection of microinjected dextran molecules labeled with the carboxymethylindocyanine dye Cy3 was a few thousand molecules per cell, and the diffusion constant of 1.7 x 10(-7) cm2/s agreed well with values measured with other methods. Based on the fluorescence signal per molecule (fpm) and the molecule number derived from autocorrelation analysis, a new method is devised to define intracellular association states. We conclude that FCM is a powerful, noninvasive method for probing molecular interactions in femtoliter volume elements within defined subcellular locations in living cells.     

Simplified Equation to Extract Diffusion Coefficients from Confocal FRAP Data

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.     

Inferences from FRAP data are model dependent: A subdiffusive analysis

Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the development of FRAP in the 1970s, many reaction-diffusion models have been used to interpret FRAP data. However, intracellular molecules are widely observed to move by anomalous subdiffusion instead of normal diffusion. In this article, we extend a popular reaction-diffusion model of FRAP to the case of subdiffusion modeled by a fractional diffusion equation. By analyzing this reaction-subdiffusion model, we show that FRAP data are consistent with both diffusive and subdiffusive motion in many scenarios. We illustrate this general result by fitting our model to FRAP data from glucocorticoid receptors in a cell nucleus. We further show that the assumed model of molecular motion (normal diffusion or subdiffusion) strongly impacts the biological parameter values inferred from a given experimentally observed FRAP curve. We additionally analyze our model in three simplified parameter regimes and discuss parameter identifiability for varying subdiffusion exponents.