Improving Parameter Inference from FRAP Data: an Analysis Motivated by Pattern Formation in the <Emphasis Type="BoldItalic">Drosophila</Emphasis> Wing Disc

Fluorescence recovery after photobleaching (FRAP) is used to obtain quantitative information about molecular diffusion and binding kinetics at both cell and tissue levels of organization. FRAP models have been proposed to estimate the diffusion coefficients and binding kinetic parameters of species for a variety of biological systems and experimental settings. However, it is not clear what the connection among the diverse parameter estimates from different models of the same system is, whether the assumptions made in the model are appropriate, and what the qualities of the estimates are. Here we propose a new approach to investigate the discrepancies between parameters estimated from different models. We use a theoretical model to simulate the dynamics of a FRAP experiment and generate the data that are used in various recovery models to estimate the corresponding parameters. By postulating a recovery model identical to the theoretical model, we first establish that the appropriate choice of observation time can significantly improve the quality of estimates, especially when the diffusion and binding kinetics are not well balanced, in a sense made precise later. Secondly, we find that changing the balance between diffusion and binding kinetics by changing the size of the bleaching region, which gives rise to different FRAP curves, provides a priori knowledge of diffusion and binding kinetics, which is important for model formulation. We also show that the use of the spatial information in FRAP provides better parameter estimation. By varying the recovery model from a fixed theoretical model, we show that a simplified recovery model can adequately describe the FRAP process in some circumstances and establish the relationship between parameters in the theoretical model and those in the recovery model. We then analyze an example in which the data are generated with a model of intermediate complexity and the parameters are estimated using models of greater or less complexity, and show how sensitivity analysis can be used to improve FRAP model formulation. Lastly, we show how sophisticated global sensitivity analysis can be used to detect over-fitting when using a model that is too complex.     

FRAP beam-size analysis to measure palmitoylation-dependent membrane association dynamics and microdomain partitioning of Ras proteins

Motions of membrane-associated proteins within and between membranes are essential for many cellular functions. We describe the application of fluorescence recovery after photobleaching (FRAP) beam-size analysis to investigate the role of palmitoylation in the membrane targeting and membrane association dynamics of H-Ras. The method described distinguishes between FRAP by lateral diffusion and by cytoplasmic exchange, and enables to obtain an estimate of the membrane affinity in live cells. These studies show distinct roles for the two palmitoylation sites (Cys181 and Cys184) on H-Ras, with different effects on membrane affinity and microlocalization.     

Glutamine rich and basic region/leucine zipper (bZIP) domains stabilize cAMP-response element-binding protein (CREB) binding to chromatin

We have examined the dynamics of cAMP-response element-binding protein (CREB) binding to chromatin in live cells using fluorescence recovery after photobleaching (FRAP). CREB was found to bind to target sites with a residence time of 100 s, and exposure to a cAMP agonist had no effect on these kinetics. In addition to the basic region/leucine zipper (bZIP) domain, a glutamine-rich trans-activation domain in CREB called Q2 also appeared to be critical for promoter occupancy. Indeed, mutations in Q2 that reduced residence time by FRAP assay disrupted target gene activation via CREB in cells exposed to a cAMP agonist. Notably, insertion of the glutamine-rich B trans-activation domain of SP1 into a mutant CREB polypeptide lacking Q2 stabilized CREB occupancy and rescued target gene activation. These results suggest a novel mechanism by which the family of glutamine-rich activators promotes cellular gene expression.     

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.     

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.     

Disruption of NAD~+ binding site in glyceraldehyde 3-phosphate dehydrogenase affects its intranuclear interactions

AIM:To characterize phosphorylation of human glyceraldehyde 3-phosphate dehydrogenase(GAPDH),and mobility of GAPDH in cancer cells treated with chemotherapeutic agents. METHODS:We used proteomics analysis to detect and characterize phosphorylation sites within human GAPDH. Site-specific mutagenesis and alanine scanning was then performed to evaluate functional significance of phosphorylation sites in the GAPDH polypeptide chain. Enzymatic properties of mutated GAPDH variants were assessed using kinetic studies. Intranuclear dynamics parameters(diffusion coefficient and the immobile fraction) were estimated using fluorescence recovery after photobleaching(FRAP) experiments and confocal microscopy. Molecular modeling experiments were performed to estimate the effects of mutations on NAD+ cofactor binding.RESULTS:Using MALDI-TOF analysis,we identified novel phosphorylation sites within the NAD+ binding center of GAPDH at Y94,S98,and T99. Using polyclonal antibody specific to phospho-T99-containing peptide within GAPDH,we demonstrated accumulation of phospho-T99-GAPDH inthe nuclear fractions of A549,HCT116,and SW48 cancer cel s after cytotoxic stress. We performed site-mutagenesis,and estimated enzymatic properties,intranuclear distribution,and intranuclear mobility of GAPDH mutated variants. Site-mutagenesis at positions S98 and T99 in the NAD+ binding center reduced enzymatic activity of GAPDH due to decreased affinity to NAD+(Km = 741 ± 257 μmol/L in T99 I vs 57 ± 11.1 μmol/L in wild type GAPDH. Molecular modeling experiments revealed the effect of mutations on NAD+ binding with GAPDH. FRAP(fluorescence recovery after photo bleaching) analysis showed that mutations in NAD+ binding center of GAPDH abrogated its intranuclear interactions. CONCLUSION:Our results suggest an important functional role of phosphorylated amino acids in the NAD+ binding center in GAPDH interactions with its intranuclear partners.     

Dissecting the binding mechanism of the linker histone in live cells: an integrated FRAP analysis

The linker histone H1 has a fundamental role in DNA compaction. Although models for H1 binding generally involve the H1 C‐terminal tail and sites S1 and S2 within the H1 globular domain, there is debate about the importance of these binding regions and almost nothing is known about how they work together. Using a novel fluorescence recovery after photobleaching (FRAP) procedure, we have measured the affinities of these regions individually, in pairs, and in the full molecule to demonstrate for the first time that binding among several combinations is cooperative in live cells. Our analysis reveals two preferred H1 binding pathways and we find evidence for a novel conformational change required by both. These results paint a complex, highly dynamic picture of H1–chromatin binding, with a significant fraction of H1 molecules only partially bound in metastable states that can be readily competed against. We anticipate the methods we have developed here will be broadly applicable, particularly for deciphering the binding kinetics of other nuclear proteins that, similar to H1, interact with and modify chromatin.     

Constitutive binding of EBNA1 protein to the Epstein-Barr virus replication origin, oriP, with distortion of DNA structure during latent infection.

Replication of the circular, 170 kb genome of Epstein-Barr virus (EBV) during latent infection is performed by the cellular replication machinery under cell-cycle control. A single viral protein, EBNA1, directs the cellular replication apparatus to initiate replication within the genetically defined replication origin, oriP, at a cluster of four EBNA1 binding sites, referred to here as the physical origin of bidirectional replication, or OBR. A second cluster of EBNA1 binding sites within oriP, the 30 bp repeats, serves an essential role as a replication enhancer and also provides a distinct episome maintenance function that is unrelated to replication. We examined the functional elements of oriP for binding by EBNA1 and possibly other proteins in proliferating Raji cells by generating in vivo footprints using two reagents, dimethylsulfate (DMS) and KMnO4. We also employed deoxyribonuclease I (DNase I) with permeabilized cells. The in vivo and permeabilized cell footprints at the EBNA1 binding sites, particularly those obtained using DMS, gave strong evidence that all of these sites are bound by EBNA1 in asynchronously dividing cells. No consistent evidence was found to suggest binding by other proteins at any other sites within the functional regions of oriP. Thymines at symmetrical positions of the OBR within oriP were oxidized when cells were treated with permanganate, suggestive of bends or other distortions of DNA structure at these positions; binding of EBNA1 in vitro to total DNA from Raji cells induced reactivity to permanganate at identical positions. The simplest interpretation of the results, which were obtained using asynchronously dividing cells, is that EBNA1 binds to its sites at oriP and holds the OBR in a distorted conformation throughout most of the cell cycle, implying that replication is initiated by a cellular mechanism and is not limited by an availability of EBNA1 for binding to oriP.     

Measurement of mass transport and reaction parameters in bulk solution using photobleaching. Reaction limited binding regime.

Fluorescence recovery after photobleaching (FRAP) has been used previously to investigate the kinetics of binding to biological surfaces. The present study adapts and further develops this technique for the quantification of mass transport and reaction parameters in bulk media. The technique's ability to obtain the bulk diffusion coefficient, concentration of binding sites, and equilibrium binding constant for ligand/receptor interactions in the reaction limited binding regime is assessed using the B72.3/TAG-72 monoclonal antibody/tumor associated antigen interaction as a model in vitro system. Measurements were independently verified using fluorometry. The bulk diffusion coefficient, concentration of binding sites and equilibrium binding constant for the system investigated were 6.1 +/- 1.1 x 10(-7) cm2/s, 4.4 +/- 0.6 x 10(-7) M, and 2.5 +/- 1.6 x 10(7) M-1, respectively. Model robustness and the applicability of the technique for in vivo quantification of mass transport and reaction parameters are addressed. With a suitable animal model, it is believed that this technique is capable of quantifying mass transport and reaction parameters in vivo.     

Challenges and artifacts in quantitative photobleaching experiments

Confocal fluorescence recovery after photobleaching (FRAP) is today the prevalent tool when studying the diffusional and kinetic properties of proteins in living cells. Obtaining quantitative data for diffusion coefficients via FRAP, however, is challenged by the fact that both bleaching and scanning take a finite time. Starting from an experimental case, it is shown by means of computer simulations that this intrinsic temporal limitation can lead to a gross underestimation of diffusion coefficients. Determining the binding kinetics of proteins to membranes with FRAP is further shown to be severely hampered by additional diffusional contributions, e.g. diffusion-limited binding. In some cases, the binding kinetics may even be masked entirely by diffusion. As current efforts to approach biological problems with biophysical models have to rely on experimentally determined model parameters, e.g. binding rates and diffusion constants, it is proposed that the accuracy in evaluating FRAP measurements can be improved by means of accompanying computer simulations.     

A quantitative approach to analyze binding diffusion kinetics by confocal FRAP

Most of the important types of interactions that occur in cells can be characterized as binding-diffusion type processes, and can be quantified by kinetic rate constants such as diffusion coefficients (D) and binding rate constants (k_on and k_off). Confocal FRAP is a potentially important tool for the quantitative analysis of intracellular binding-diffusion kinetics, but how to dependably extract accurate kinetic constants from such analyses is still an open question. To this end, in this study, we developed what we believe is a new analytical model for confocal FRAP-based measurements of intracellular binding-diffusion processes, based on a closed-form equation of the FRAP formula for a spot photobleach geometry. This approach incorporates a binding diffusion model that allows for diffusion of both the unbound and bound species, and also compensates for binding diffusion that occurs during photobleaching, a critical consideration in confocal FRAP analysis. In addition, to address the problem of parametric multiplicity, we propose a scheme to reduce the number of fitting parameters in the effective diffusion subregime when D's for the bound and unbound species are known. We validate this method by measuring kinetic rate constants for the CAAX-mediated binding of Ras to membranes of the endoplasmic reticulum, obtaining binding constants of k_on ∼ 255/s and k_off ∼ 31/s.     

Characterization of Cell Boundary and Confocal Effects Improves Quantitative FRAP Analysis

Fluorescence recovery after photobleaching (FRAP) is an important tool used by cell biologists to study the diffusion and binding kinetics of vesicles, proteins, and other molecules in the cytoplasm, nucleus, or cell membrane. Although many FRAP models have been developed over the past decades, the influence of the complex boundaries of 3D cellular geometries on the recovery curves, in conjunction with regions of interest and optical effects (imaging, photobleaching, photoswitching, and scanning), has not been well studied. Here, we developed a 3D computational model of the FRAP process that incorporates particle diffusion, cell boundary effects, and the optical properties of the scanning confocal microscope, and validated this model using the tip-growing cells of Physcomitrella patens. We then show how these cell boundary and optical effects confound the interpretation of FRAP recovery curves, including the number of dynamic states of a given fluorophore, in a wide range of cellular geometries—both in two and three dimensions—namely nuclei, filopodia, and lamellipodia of mammalian cells, and in cell types such as the budding yeast, Saccharomyces pombe, and tip-growing plant cells. We explored the performance of existing analytical and algorithmic FRAP models in these various cellular geometries, and determined that the VCell VirtualFRAP tool provides the best accuracy to measure diffusion coefficients. Our computational model is not limited only to these cells types, but can easily be extended to other cellular geometries via the graphical Java-based application we also provide. This particle-based simulation—called the Digital Confocal Microscopy Suite or DCMS—can also perform fluorescence dynamics assays, such as number and brightness, fluorescence correlation spectroscopy, and raster image correlation spectroscopy, and could help shape the way these techniques are interpreted.