Artifact-Free and Detection-Profile-Independent Higher-Order Fluorescence Correlation Spectroscopy for Microsecond-Resolved Kinetics. 2. Mixtures and Reactions

There is more to scanning than meets the eye: Raster Image Correlation Spectroscopy

Raster Image Correlation Spectroscopy (RICS) is a confocal image analysis method that can measure the diffusion and interactions of fluorescently labeled molecules in real time in solution and in living cells. RICS is easy to implement on commercial confocal microscopes and allows detailed investigations of complex biological systems and pathways. The method is especially robust for measurements in living cells using commonly used labels such as fluorescent proteins. Moreover, since its invention in 2005, the robustness and applicability of RICS has been significantly increased to allow, e.g., straightforward kinetic analyses, advanced image segmentation, parameter mapping, and multi-species analysis. In this review, we describe the methodological principles of RICS in a manner that is accessible to a broad readership, position RICS in relation to other fluorescence fluctuation techniques, highlight recent methodological advances and present exemplary applications of the method. With this review, we hope to facilitate the implementation of this powerful method into the everyday repertoire of confocal imaging approaches.

Efficient, nonparametric removal of noise and recovery of probability distributions from time series using nonlinear-correlation functions: Photon and photon-counting noise

A preceding paper [M. Dhar, J. A. Dickinson, and M. A. Berg, J. Chem. Phys. 159, 054110 (2023)] shows how to remove additive noise from an experimental time series, allowing both the equilibrium distribution of the system and its Green's function to be recovered. The approach is based on nonlinear-correlation functions and is fully nonparametric: no initial model of the system or of the noise is needed. However, single-molecule spectroscopy often produces time series with either photon or photon-counting noise. Unlike additive noise, photon noise is signal-size correlated and quantized. Photon counting adds the potential for bias. This paper extends noise-corrected-correlation methods to these cases and tests them on synthetic datasets. Neither signal-size correlation nor quantization is a significant complication. Analysis of the sampling error yields guidelines for the data quality needed to recover the properties of a system with a given complexity. We show that bias in photon-counting data can be corrected, even at the high count rates needed to optimize the time resolution. Using all these results, we discuss the factors that limit the time resolution of single-molecule spectroscopy and the conditions that would be needed to push measurements into the submicrosecond region.

Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.

Resolving fluorescent species by their brightness and diffusion using correlated photon-counting histograms

Fluorescence fluctuation spectroscopy (FFS) refers to techniques that analyze fluctuations in the fluorescence emitted by fluorophores diffusing in a small volume and can be used to distinguish between populations of molecules that exhibit differences in brightness or diffusion. For example, fluorescence correlation spectroscopy (FCS) resolves species through their diffusion by analyzing correlations in the fluorescence over time; photon counting histograms (PCH) and related methods based on moment analysis resolve species through their brightness by analyzing fluctuations in the photon counts. Here we introduce correlated photon counting histograms (cPCH), which uses both types of information to simultaneously resolve fluorescent species by their brightness and diffusion. We define the cPCH distribution by the probability to detect both a particular number of photons at the current time and another number at a later time. FCS and moment analysis are special cases of the moments of the cPCH distribution, and PCH is obtained by summing over the photon counts in either channel. cPCH is inherently a dual channel technique, and the expressions we develop apply to the dual colour case. Using simulations, we demonstrate that two species differing in both their diffusion and brightness can be better resolved with cPCH than with either FCS or PCH. Further, we show that cPCH can be extended both to longer dwell times to improve the signal-to-noise and to the analysis of images. By better exploiting the information available in fluorescence fluctuation spectroscopy, cPCH will be an enabling methodology for quantitative biology.

In situ study of RSK2 kinase activity in a single living cell by combining single molecule spectroscopy with activity-based probes

FCS with the ABP strategy is a very promising method for studying endogenous protein kinases in living cells.

Quantifying Release from Lipid Nanocarriers by Fluorescence Correlation Spectroscopy

Understanding the release of drugs and contrast agents from nanocarriers is fundamental in the development of new effective nanomedicines. However, the commonly used method based on dialysis frequently fails to quantify the release of molecules poorly soluble in water, and it is not well-suited for in situ measurements in biological media. Here, we have developed a new methodology for quantifying the release of fluorescent molecules from lipid nanocarriers (LNCs) using fluorescence correlation spectroscopy (FCS). LNCs based on nanoemulsion droplets, encapsulating the hydrophobic Nile red derivative NR668 as a model cargo, were used. Our studies revealed that the standard deviation of fluorescence fluctuations in FCS measurements depends linearly on the dye loading in the nanocarriers, and it is insensitive to the presence of less-bright molecular emissive species in solution. In sharp contrast, classical FCS parameters, such as the number and the brightness of emissive species, are strongly influenced by the fluorescence of molecular species in solution. Therefore, we propose to use the standard deviation of fluorescence fluctuations for the quantitative analysis of dye release from nanocarriers, which is unaffected by the "parasite" fluorescence of the released dyes or the auto-fluorescence of the medium. Using this method, we found that LNCs remain intact in water, whereas in serum medium, they release their content in a temperature-dependent manner. At 37 °C, the release was relatively slow reaching 50% only after 6 h of incubation. The results are corroborated by qualitative observations based on Förster resonance energy transfer between two different encapsulated dyes. The developed method is simple because it is only based on the standard deviation of fluorescence fluctuations and, in principle, can be applied to nanocarriers of different types.

Fluorescence-based monitoring of electronic state and ion exchange kinetics with FCS and related techniques: from T-jump measurements to fluorescence fluctuations

In this review, we give a historical view of how our research in the development and use of fluorescence correlation spectroscopy (FCS) and related techniques has its roots and how it originally evolved from the pioneering work of Manfred Eigen, his colleagues, and coworkers. Work on temperature-jump (T-jump) experiments, conducted almost 50 years ago, led on to the development of the FCS technique. The pioneering work in the 1970s, introducing and demonstrating the concept for FCS, in turn formed the basis for the breakthrough use of FCS more than 15 years later. FCS can be used for monitoring reaction kinetics, based on fluctuations at thermodynamic equilibrium, rather than on relaxation measurements following perturbations. In this review, we more specifically discuss FCS measurements on photodynamic, electronic state transitions in fluorophore molecules, and on proton exchange dynamics in solution and on biomembranes. In the latter case, FCS measurements have proven capable of casting new light on the mechanisms of proton exchange at biological membranes, of central importance to bioenergetics and signal transduction. Finally, we describe the transient-state (TRAST) spectroscopy/imaging technique, sharing features with both relaxation (T-jump) and equilibrium fluctuation (FCS) techniques. TRAST is broadly applicable for cellular and molecular studies, and we briefly outline how TRAST can provide unique information from fluorophore blinking kinetics, reflecting e.g., cellular metabolism, rare molecular encounters, and molecular stoichiometries.