Biophysical Reports

FRET imaging is an essential analytical method in biomedical research. The limited photon-budget experimentally available, however, imposes compromises between spatiotemporal and biochemical resolutions, photodamage and phototoxicity. The study of photon-statistics in biochemical imaging is thus important in guiding the efficient design of instrumentation and assays. Here, we show a comparative analysis of photon-statistics in FRET imaging demonstrating how the precision of FRET imaging varies vastly with imaging parameters. Therefore, we provide analytical and numerical tools for assay optimization. FLIM is a very robust technique with excellent photon-efficiencies but also intensity-based FRET imaging can reach very high precision by utilizing also information within acceptor fluorescence.

Many transient processes in cells arise from the binding of cytosolic proteins to membranes. Quantifying this membrane binding and its associated diffusion in the living cell is therefore of primary importance. Dynamic photonic microscopies, e.g. single/multiple particle tracking, fluorescence recovery after photobleaching and fluorescence correlation spectroscopy (FCS) enable noninvasive measurement of molecular mobility in living cells and their plasma membranes. However, FCS with a single beam waist is of limited applicability with complex, non Brownian, motions. Recently, the development of FCS diffusion laws methods has given access to the characterization of these complex motions, although none of them is applicable to the membrane binding case at the moment. In this study, we combined computer simulations and FCS experiments to propose an FCS diffusion law for membrane binding. First, we generated computer simulations of spot-variation FCS (svFCS) measurements for a membrane binding process combined to 2D and 3D diffusion at the membrane and in the bulk/cytosol, respectively. Then, using these simulations as a learning set, we derived an empirical diffusion law with three free parameters: the apparent binding constant KDapp, the diffusion coefficient on the membrane D2D and the diffusion coefficient in the bulk/cytosol, D3D. Finally, we monitored, using svFCS, the dynamics of retroviral Gag proteins and associated mutants during their binding to supported lipid bilayers of different lipid composition or at plasma membranes of living cells and we quantified KDapp and D2D in these conditions using our empirical diffusion law. Based on these experiments and numerical simulations, we conclude that this new approach enables correct estimation of membrane partitioning and membrane diffusion properties (KDapp and D2D) for peripheral membrane molecules.

Molecular plasma membrane organization and dynamics play an important role in cellular signalling. Advances in our understanding of the nanoscale architecture of the plasma membrane heavily rely on the development of non-invasive experimental methods, particularly of advanced fluorescence microscopy and spectroscopy techniques with high spatio-temporal resolution and sensitivity to local molecular properties. However, it remains difficult to combine several of them for a multimodal characterisation that would reduce the possibility of misinterpretations. Here, we integrated a spectral detector into a super-resolution stimulated emission depletion (STED) microscope, achieving three goals. First, we show that compared to the standard ratiometric detection using fixed bandpass filters, the spectrally resolved acquisition together with spectral fitting or phasor analysis improves the accuracy of experiments determining membrane lipid order with polarity-sensitive probes multifold. Secondly, we demonstrate that this acquisition scheme allows the use of such probes in combination with other dyes with overlapping spectra, enabling co-localisation of the membrane order maps with other cellular structures of interest, e.g. fluorescently labelled proteins. Finally, we correlate the obtained membrane lipid order with the anomalous trapped diffusion properties of a fluorescent sphingomyelin lipid analogue in the plasma membrane of living cells, as determined by STED fluorescence correlation spectroscopy, and highlight that some of the most apparent trapping sites locate at the boundaries of local ordered environments discernible by the introduced spectral STED microscopy. With additional measurements in model membranes and Monte-Carlo simulations we conclude that for sub-100 nm ordered environments uneven probe partitioning cannot by itself explain the trapping diffusion of SM in cells.

Fluorescence recovery after photobleaching (FRAP) is broadly used to investigate the dynamics of molecules in cells and tissues, notably to quantify diffusion coefficients. FRAP is based on the spatiotemporal imaging of fluorescent molecules following an initial bleaching of fluorescence in a region of the sample. Although a large number of methods have been developed to infer kinetic parameters from experiments, it is still a challenge to fully characterize molecular dynamics from noisy experiments in which diffusion is coupled to other molecular processes or in which the initial bleaching profile is not perfectly controlled. To address this challenge, we have developed HiFRAP to quantify the reaction-(or exchange-)diffusion kinetic parameters from FRAP under imperfect experimental conditions. HiFRAP is based on a low-rank approximation of a kernel related to the model Greens function and is implemented as an ImageJ/Python macro for (potentially curved) one-dimensional systems and for two-dimensional systems. To the best of our knowledge, HiFRAP offers features that have not been combined together: making no assumption on the initial bleaching profile, which does not need to be known; accounting for the limitation of the optical setup by diffraction; inferring several kinetic parameters from a single experiment; providing errors on parameter estimation; and testing model goodness. In the future, our approach could be applied to other dynamical processes described by linear partial differential equations, which could be useful beyond FRAP, in experiments where the concentration fields are monitored over space and time. SIGNIFICANCEFluorescence recovery after photobleaching (FRAP) is a microscopy approach that is widely used to investigate the diffusion and transport of molecules in life sciences and in material sciences. Numerous methods have been developed to derive kinetic parameters such as diffusion and binding coefficients. However, these methods suffer from limitations associated with experimental constraints, such as technical noise or an imperfectly known initial condition. To circumvent these limitations, we developed a comprehensive approach to estimate several kinetic parameters from a single experiment, to assess the precision of estimation, and to test whether the underlying model is well-suited. We implemented this approach in HiFRAP, an ImageJ/Python macro of broad applicability to one- and two-dimensional systems.

Fluorescence correlation spectroscopy (FCS) is a valuable tool to study the molecular dynamics of living cells. When used together with a super-resolution stimulated emission depletion (STED) microscope, STED-FCS can measure diffusion processes at the nanoscale in living cells. In twodimensional (2D) systems like the cellular plasma membrane, a ring-shaped depletion focus is most commonly used to increase the lateral resolution, leading to more than 25-fold decrease in the observation volumee, reaching the relevant scale of supramolecular arrangements. However, STED-FCS faces severe limitations when measuring diffusion in three dimensions (3D), largely due to the spurious background contributions from undepleted areas of the excitation focus that reduce the signal quality and ultimately limit the resolution. In this paper, we investigate how different STED confinement modes can mitigate this issue. By simulations as well as experiments with fluorescent probes in solution and in cells, we demonstrate that the coherent-hybrid (CH) depletion pattern reduces background most efficiently and thus provides superior signal quality under comparable reduction of the observation volume. Featuring also the highest robustness to common optical aberrations, CH-STED can be considered the method of choice for reliable STED-FCS based investigations of 3D diffusion on the sub-diffraction scale.

Fluorescence recovery after photobleaching (FRAP) is widely used to characterize diffusion in cells, but quantitative interpretation of the data in small prokaryotes requires explicitly accounting for cell geometry. While this has been successfully achieved for spherical and rod-shaped bacteria, analytical approaches developed in these cases are not directly applicable to cells with more complex morphologies. Here, we explore the application of FRAP to helical bacteria using simulations. We show that half-compartment FRAP experiments, where one-half of the cell is photobleached, provide a robust means of characterizing fast protein diffusion. To help with the practical implementation of this technique, we established the relationship between the diffusion coefficient and characteristic fluorescence recovery time as a function of cell length and helical parameters, and for two different ways of estimating the recovery time. As a first application, we report measurements of the diffusion coefficient of the fluorescent protein, mNeonGreen, in the helical bacterium Paramagnetospirillum magneticum AMB-1. We find it to be D = 4.9 {+/-} 2.2 {micro}m2 s-1 in isosmotic conditions, not significantly different from the value measured in Escherichia coli. Although developed for helical bacteria, including spirilla, spirochetes, and vibrios, our framework can readily be extended to cells or compartments with other geometries.

Flipper-TR is a membrane dye sensitive to lipid packing widely used to probe membrane tension in live cells via fluorescence lifetime imaging microscopy (FLIM). However, no consensus currently exists on the optimal strategy for extracting lifetime values, particularly across varying experimental setups and biological systems. Here, we systematically compare multiple approaches to estimate Flipper-TR lifetime, including multi-exponential reconvolution fitting, tail fitting, mean photon arrival time (first moment), and phasor analysis. These estimators are tested against changes in photon budget, sample characteristics, microscope manufacturer, and laser frequency. This offers a comprehensive benchmark and decision-making framework for quantitative FLIM analysis of Flipper dyes in various contexts.

Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of molecular kinetic processes. The mathematical frameworks of both fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis, which can measure these fluctuations, assume an infinite Gaussian beam, which prevents their application to particles within domains bounded at the nanoscale. We therefore derived general forms of FCS and PCH for bounded systems. The finite domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case of molecules confined by two boundaries under Gaussian beams. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible, including in the one-dimensional lipid tubules discussed in Part 2 of this paper. Statement of SignificanceMethods based on fluorescence measurements of molecular concentration fluctuations, including Fluorescence Correlation Spectroscopy and Photon Count Histogram analysis, are widely used to determine rates of diffusion, chemical reaction and sizes of molecular aggregates. Typically, the range over which the molecules can diffuse is large compared to the size of the focused laser beam that excites the fluorescence. This work extends these measurements to systems that are comparable in size to the excitation laser beam. This extends the application of these methods to very small samples such as the interior of bacterial cells or the diffusion of molecules along individual macromolecules such as DNA.

Quantitative fluorescence emission anisotropy microscopy reveals the organization of fluorescently labelled cellular components and allows for their characterization in terms of changes in either rotational diffusion or homo-Forsters energy transfer characteristics in living cells. These properties provide insights into molecular organization, such as orientation, confinement and oligomerization in situ. Here we elucidate how quantitative measurements of anisotropy using multiple microscope systems may be made, by bringing out the main parameters that influence the quantification of fluorescence emission anisotropy. We focus on a variety of parameters that contribute to errors associated with the measurement of emission anisotropy in a microscope. These include the requirement for adequate photon counts for the necessary discrimination of anisotropy values, the influence of extinction coefficients of the illumination source, the detector system, the role of numerical aperture and excitation wavelength. All these parameters also affect the ability to capture the dynamic range of emission anisotropy necessary for quantifying its reduction due to homo-FRET and other processes. Finally, we provide easily implementable tests to assess whether homo-FRET is a cause for the observed emission depolarization.

Single-particle tracking methods have emerged as a crucial tool for the characterization of dynamical and diffusive processes in a range of biological and synthetic systems. Here, we propose a simple and light-weight yet accurate method for the segmentation of multi-state Brownian trajectories based on an optimised Gaussian filtering of the displacement time series combined with an automated fitting to a Gaussian mixture model. We verify our method using synthetic, 2-state Brownian trajectories and show that our method provides high levels of accuracy in terms of segmentation and the estimation of self-diffusion coefficients for reasonably well-separated values of the diffusion coefficients. We furthermore demonstrate the feasibility of our method on experimental systems using single-particle tracking data for diffusing membrane proteins bound to a supported lipid bilayer. Compared to methods based on deep learning or hidden Markov models our method imposes a much lower computational load, making it suitable for fast and accurate online processing of single-particle trajectories from microscopy images.

Fluorescent reporters such as fluorescent proteins or chemigenetic indicators are indispensable tools for studying biological processes using light microscopy. Choosing an appropriate fluorescent tag is a crucial step in experimental design not only for imaging but also for quantitative measurements such as fluorescence fluctuation spectroscopy. Two key parameters should be considered: Fluorescent brightness and photo-bleaching. Change to fluorescence intensity due to photobleaching is relatively easy to assess in different biological environments, while brightness is more elusive. Here, we develop and employ a fluorescence correlation spectroscopy (FCS) based excitation scan assay that determines fluorescent protein performance and validate it in tissue culture and zebrafish embryos. We employ our FCS pipeline to compare a set of 10 established fluorescent proteins as well as HALO and SNAP tags for both cellular imaging and measurements of diffusion dynamics with FCS. We show that mNeonGreen outperforms mEGFP in tissue culture and zebrafish embryos. We also compare StayGold variants against other green fluorescent proteins and chemigenetic reporters in tissue culture. Overall, we present a broadly applicable approach for determining fluorescent reporter brightness in the living system of interest.

Discerning two or more identical and constantly scattering point sources using freely propagating waves is thought to be limited by diffraction. Here we show both theoretically and experimentally that by employing a diffraction minimum rather than a maximum for resolution, a given number of point scatterers can be discerned at tiny fractions of the employed wavelength. Specifically, we identify an 8 nm distance between two constantly emitting (non-blinking, non-switchable) fluorescent molecules, corresponding to 1/80 of the wavelength. Moreover, we show that contrary to naive expectations, the measurement precision improves with decreasing distance between the scatterers and with increased scatterer density, thus opening up the prospect of resolving clusters of (optical) point scatterers at tiny fractions of the wavelength.

Fluorescence spectroscopic and imaging techniques, such as fluorescence-correlation spectroscopy, image correlation spectroscopy, time-resolved fluorescence spectroscopy, and intensity-based spectroscopy, can provide sparse time-dependent positional and inter-fluorophore distance information for macromolecules and their complexes in vitro and in living cells. Here, we formulated a Bayesian framework for processing and using the fluorescence data for interpreting by static and dynamic models of biomolecules. We introduce Bayesian Fluorescence Framework (BFF) as part of the open-source Integrative Modeling Platform (IMP) software environment, facilitating the development of modeling protocols based in part on fluorescence data. BFF improves the accuracy, precision, and completeness of the resulting models by formulating the modeling problem as a sampling problem dependent on general and flexible libraries of (i) atomic and coarse-grained molecular representations of single-state models, multi-state models, and dynamic processes, (ii) Bayesian data likelihoods and priors, as well as (iii) sampling schemes. To illustrate the framework, we apply it to a sample synthetic single-molecule FRET dataset of the human transglutaminase 2. We show how to integrate time-resolved fluorescence intensities, fluorescence correlation spectroscopy curves, and fluorescence anisotropies to simultaneously resolve dynamic structures, state populations, and molecular kinetics. As BFF is part of IMP, fluorescence data can be easily integrated with other data types to solve challenging modeling problems. Statement of SignificanceBayesian Framework for Fluorescence (BFF) is software that implements a probabilistic framework for processing experimental fluorescence data to provide input information for Bayesian integrative structure modeling. BFF facilitates constructing integrative modeling protocols based in part on fluorescence data by reducing the required fluorescence spectroscopy and microscopy domain knowledge. In addition, it improves the precision and accuracy of the resulting models.

Forster Resonance Energy Transfer (FRET) is a powerful technique for the detection and characterization of biomolecular interactions and conformational changes with sub-nanometer spatial resolution and a temporal resolution down to the timescale of fluorescence. While the technique is widely adopted in structural biology and biophysics, the evolution of single-molecule FRET has led to experimental setups with sophisticated optical layouts, multi-laser excitation schemes and time-resolved detection electronics. We here present an accessible alternative towards single-molecule FRET based on Brick-MIC, a recently introduced 3D-printed micro-spectroscopy platform. The FRET-Brick uses continuous-wave excitation at 488 nm with a minimal set of opto-mechanical components and photomultiplier detectors (PMTs). With this we were able to significantly reduce the setup complexity retaining single-molecule sensitivity with dyes matching the sensitivity of PMTs. To maximize the photon output of Alexa488, ATTO488 (donors), Alexa555, ATTO542 and Cy3B (acceptors), we introduce ferrocene-derivatives as photostabilizers that increase both dye brightness and remove dark-states. We benchmark the performance of the FRET-Brick with fluorophore-labelled oligonucleotide reference structures also in comparison to accessible volume simulations, and by detecting conformational changes in bacterial substrate binding proteins. Our work demonstrates that qualitative and quantitative smFRET measurements are possible with the minimalistic and cost-effective FRET-Brick.

Single-molecule microscopy has been widely used to study the structure and dynamics of RNA, but extension to larger systems such as long non-coding RNA (lncRNA) has proven challenging. Methods such as single-molecule kinetic analysis of RNA transient structure (SiM-KARTS), where the binding of a short, complementary oligonucleotide probe is used to determine accessibility of a specific region of the RNA, are promising. However, adapting SiM-KARTS to systems as complex as lncRNA requires careful optimization of experimental variables that have not been thoroughly explored. In this work, SiM-KARTS, thermal denaturation experiments, and circular dichroism spectroscopy were used to analyze the binding behaviors of probes with alternative backbone chemistries, specifically DNA with locked nucleic acid (LNA) residues incorporated and morpholinos. A segment of lncRNA that enabled control over the accessibility of the target sequence was used as a model. We show that optimizing probe backbone chemistry can allow for a more precise distinction between different structures of the target RNA, and for fine-tuning of probe binding stability without the structural impacts that other variables such as ionic concentration may have. Specifically, we demonstrate that LNA probes exhibit a high degree of structural sensitivity in both their binding and unbinding kinetics. We further show that when binding and unbinding rates are considered holistically, LNA probes allow traces arising from different target RNA structures to be individually classified with a high degree of accuracy. These results provide design principles for the application of SiM-KARTS to target RNAs of increased complexity such as lncRNA.

Single molecule fluorescence localization with minimum photon flux imaging (MINFLUX) can achieve localization precisions in the small nanometer range or better under suitable conditions. Potentially adverse conditions, such as a fixed fluorescence dipole or optical aberrations, that could cause systematic localization errors, have received little attention up to now. Here, we study these effects in simulation. We find that biases occur for fluorophores with a fixed absorption dipole tilted out of the imaging plane. These become larger (up to about 25% of the diameter of the circle spanned by the doughnut center positions) the larger the tilt angle gets. As a rule of thumb the spread in bias is smaller than 5 nm in case the dipole orientation is less than 30{degrees} out of plane for the typical case of a doughnut probing circle of diameter 100 nm. For freely rotating dipoles only the primary aberrations astigmatism and coma contribute to bias. This bias depends on the position of the fluorophore inside the circular probing area of MINFLUX and can be significantly larger than the localization precision. We show that increasing the number of measurements over the circle from a triangular to a hexagonal pattern is beneficial for reducing bias in all cases. Iterative shrinking of the probing area can eliminate the position dependent bias completely, but a strong dependence on dipole orientation of the bias at the center of the probing area remains.

Biological systems are regulated by molecular interactions which are tuned by the concentrations of each of the molecules involved. Cells exploit this feature by regulating protein expression, to adapt their responses to overstimulation. Correlating events in single cells to the concentrations of proteins involved can therefore provide important mechanistic insight into cell behavior. Unfortunately, quantification of molecular densities by fluorescence imaging becomes non-trivial due to the diffraction limited resolution of the imaged volume. We show here an alternative approach to overcome this limitation in optical quantification of protein concentrations which is based on calibrating protein volume and surface densities in a model membrane system. We exploit the ability of fluorescently labeled annexin V to bind membranes in presence of calcium. By encapsulating known concentrations of annexin V, we can directly infer the membrane density of annexin V after addition of Ca2+ and correlate the density with the measured fluorescence signal. Our method, named Calmet, enables quantitative determination of the concentration of cytosolic and membrane associated proteins. The applicability of Calmet is demonstrated by quantification of a transmembrane protein receptor (beta 1 adrenergic receptor) labeled by SNAP tagged fluorophores and expressed in HEK293 cells. Calmet is a generic method suitable for the determination of a broad range of concentrations and densities and can be used on regular fluorescence images captured by confocal laser scanning microscopy.

The stoichiometry of molecular components within supramolecular biological complexes is often an important property to understand their biological functioning, particularly within their native environment. While there are well established methods to determine stoichiometry in vitro, it is presently challenging to precisely quantify this property in vivo, especially with single molecule resolution that is needed for the characterization stoichiometry heterogeneity. Previous work has shown that optical microscopy can provide some information to this end, but it can be challenging to obtain highly precise measurements at higher densities of fluorophores. Here we provide a simple approach using already established procedures in single-molecule localization microscopy (SMLM) to enable precise quantification of stoichiometry within individual complexes regardless of the density of fluorophores. We show that by focusing on the number of fluorophore detections accumulated during the quasi equilibrium-state of this process, this method yields a 50-fold improvement in precision over values obtained from images with higher densities of active fluorophores. Further, we show that our method yields more correct estimates of stoichiometry with nuclear pore complexes and is easily adaptable to quantify the DNA content with nanodomains of chromatin within individual chromosomes inside cells. Thus, we envision that this straightforward method may become a common approach by which SMLM can be routinely employed for the accurate quantification of subunit stoichiometry within individual complexes within cells.

Understanding protein oligomerization in living cells is essential for elucidating cellular signaling and regulation, yet quantitative analysis remains challenging due to heterogeneous expression levels, dynamic interactions, and limited access to absolute protein concentrations. Here, we present a standardized, open-source framework for quantifying protein assemblies in living cells by integrating fluorescence lifetime and anisotropy imaging (heteroFRET and homoFRET) with molecular brightness-based concentration estimation and image analysis. Using natural variants of a vertebrate GPCR, the melanocortin-4 receptor (MC4R-A and MC4R-B2), as a model system, we demonstrate how to discriminate monomers, dimers, and higher-order oligomers, extract inter-fluorophore distance distributions, and determine association constants under physiologically relevant conditions in living cells. Standard fluorescent protein tags report on proximity and oligomerization via Homo- and HeteroFRET. Association constants are quantified using the variable protein expression in living cells and the spectroscopy readouts. By high-content imaging we overcome the biological noise and attain data qualities comparable to conventional biochemical in vitro assays. Intensity- and fluctuation-based segmentation further extends the accessible concentration range within individual cells, improving affinity analysis robustness. Our results establish quantitative image spectroscopy on living cells as quantitative tool for investigating protein-protein interactions under physiologically relevant conditions. All computational workflows are implemented in open-source software and are accompanied by detailed protocols and analysis scripts, enabling reproducible application and adaptation. Beyond GPCRs, this framework provides a practical and transferable methodology for quantitative studies on protein-protein interactions, mechanistic studies and drug discovery in complex cellular environments.

Deciphering the spatiotemporal coordination between nuclear functions is important to understand its role in the maintenance of human genome. In this context, superresolution microscopy has gained considerable interest as it can be used to probe the spatial organization of functional sites in intact single cell nuclei in the 20-250 nm range. Among the methods that quantify colocalization from multicolor images, image cross-correlation spectroscopy (ICCS) offers several advantages, namely it does not require a pre-segmentation of the image into objects and can be used to detect dynamic interactions. However, the combination of ICCS with super-resolution microscopy has not been explored yet.\n\nHere we combine dual color stimulated emission depletion (STED) nanoscopy with ICCS (STED-ICCS) to quantify the nanoscale distribution of functional nuclear sites. We show that STED-ICCS provides not only a value of colocalized fraction but also the characteristic distances associated to correlated nuclear sites. As a validation, we quantify the nanoscale spatial distribution of three different pairs of functional nuclear sites in MCF10A cells. As expected, transcription foci and a transcriptionally repressive histone marker (H3K9me3) are not correlated. Conversely, nascent DNA replication foci and the Proliferating cell nuclear antigen (PCNA) protein have a high level of proximity and are correlated at a nanometer distance which is close to the limit of our experimental approach. Finally, transcription foci are found at a distance of 130 nm from replication foci, indicating a spatial segregation at the nanoscale. Overall, our data demonstrate that STED-ICCS can be a powerful tool for the analysis of nanoscale distribution of functional sites in the nucleus.\n\nStatement of significanceSeveral methods are available to quantify the proximity of two labeled molecules from dual color images. Among them, image cross-correlation spectroscopy (ICCS) is attractive as it does not require a pre-segmentation of the image into objects and can be used to detect dynamic interactions. Here, we combine for the first time ICCS with superresolution stimulated emission depletion (STED) microscopy (STED-ICCS) to quantify the spatial distribution of functional sites in the nucleus. Our results show that STED-ICCS, in addition to quantifying the colocalized fraction, detects characteristic nanometer distances associated to correlated nuclear sites. This work shows that STED-ICCS can be a powerful tool to quantify the nanoscale distribution of functional sites in the nucleus.