Fluorescence fluctuation spectroscopy in living cells
R.A. Migueles-Ramirez1, A.G. Velasco-Felix1, R. Pinto-Cmara1, C.D. Wood1, A. Guerrero*,1 1Laboratorio Nacional de Microscopa Avanzada, Instituto de Biotecnologa. Universidad Nacional Autnoma de Mxico,
62210 Cuernavaca, Morelos, Mxico. *Author for correspondence (email@example.com).
Recent developments in fluorescence microscopy have opened the path to quantitatively describe cellular processes in living cells at the molecular level, through characterization of concentration, stoichiometry, diffusion, transport and binding amongst other parameters. Here we review the basic principles of fluorescence fluctuation spectroscopy techniques and for each section we present application examples of these techniques to living cells. Altogether, this mini review provides a comprehensive panorama of the principles behind microscopic spectroscopy techniques as well as some practical considerations for their application.
Keywords: Fluorescence Fluctuation Spectroscopy, Fluorescence Correlation Spectroscopy (FCS), Raster Image Correlation Spectroscopy (RICS), Cross-Correlation Spectroscopy (FCCS, RICCS), image Mean Square Displacement (iMSD), Number and Brightness Analysis (N&B), Photon Counting Histogram (PCH).
Living systems are subject to tireless and incessant change. Because lifes processes occur at the molecular scale, the thermally-driven random motion of molecules is a major influence governing biochemical reactions. The rate and location at which these reactions occur are affected by molecular crowding . The diffusive behavior of a molecule in the cell environment depends on the structure of the molecule itself, on the physical properties of its environment and on its molecular interactions. Diffusive motion is always present at molecular length scales, and biological systems must exploit, tolerate, or inhibit Brownian motion to perform directed and timed biochemical processes. A host of techniques have been developed to scrutinize diffusive dynamics within cells, for example fluorescence recovery after photobleaching (FRAP), single-particle tracking (SPT), and fluorescence correlation spectroscopy (FCS). FRAP depends on the capability to rapidly photobleach fluorophores within a defined region (usually in the range of a micron) in the imaging field using a high-energy laser pulse. After the laser pulse, photobleached fluorophores within the irradiated region are replaced by diffusive exchange with unbleached fluorophores from outside the irradiated region. By analyzing the dynamics of the recovery of fluorescence, it is possible to extract features of the diffusive properties of the fluorophore , . Despite its potential, the phototoxicity of the laser pulse makes FRAP a rather invasive technique . A more direct technique for monitoring diffusive dynamics is the explicit tracking of particles, through individual trajectory mapping . The experimental design involves video microscopy, in which moving species of interest are visualized at fixed time intervals. Single particle tracking has been applied to the study of a wide variety of phenomena ranging from single cell locomotion to the wandering of individual proteins in organelles . Fluorescence correlation spectroscopy is a non-invasive optical technique of great utility for probing diffusive dynamics within cells. In FCS, the fluorescence intensity in a small volume (~1 fl) is measured as a function of time  . The intensity of the recorded signal fluctuates as the fluorescent molecules enter and leave the region under observation. By analyzing the temporal fluctuations of the intensity using time- or space- dependent correlation functions, the diffusion coefficient and other characteristics of the molecular motion can be unveiled. In this mini-review, we present a selection of FCS-derived techniques which are valuable for studying how crowding alters both molecular equilibria and kinetics within the milieu of living cells. We will explore specific cases of how cell structure information can be recovered by examining deviations from the expected diffusive behavior of fluorophores in dilute solutions. Depending on the phenomenon of interest, we might be interested in the diffusion, the molecular interactions, or a combination of both. We will explain how this information can be obtained through statistical analysis of either the duration or the amplitude of the fluorescence fluctuations.
2. Unveiling molecular mobility
The number of particles diffusing through an open volume fluctuates according to a Poisson distribution . The average number of particles depends on the concentration and size of the volume. By considering independency between molecular displacements, the probability for several molecules to simultaneously leave is small compared to the probability of having a single molecule leave the observation volume. The former probability is lesser, as it results from the product of the probabilities of individual molecules leaving the observation volume. The information relating to molecular displacement is stored in the temporal structure of the signal itself. Hence, the analysis of a fluctuation
Microscopy and imaging science: practical approaches to applied research and education (A. Mndez-Vilas, Ed.)
experiment as a function of time provides single molecule information and can be unveiled by calculating its auto-correlation function. In this section we will discuss three different techniques that focus on the temporal behavior of the fluorescence fluctuations to determine the diffusion coefficient and the average number of particles. As mentioned before, FCS is based on the autocorrelation function to analyze the diffusive behavior of fluorescent particles within a fixed observation volume. Based on the FCS principle and taking advantage of the commercially available laser scanning microscopes, another technique called Raster Image Correlation Spectroscopy was developed . In this technique, the laser beam is used to scan a defined area of the sample thus allowing us to obtain not only temporal, but spatial information . In the cellular environment, molecular diffusion can sometimes present anomalous features which can be caused by crowding, binding or molecular confinement. The Image Mean Squared displacement is a powerful technique to help characterize the molecular diffusion by analyzing the distance a molecule travels in a given lapse of time.
2.1. FCS principles and theory
Fluorescence correlation spectroscopy (FCS) is a technique with high spatial and temporal resolution used to analyze the kinetics of particles diffusing at low concentrations  . Fluorescently labeled molecules in solution move randomly, with each particle following a unique trajectory. These molecules are excited as they transit through a small focal volume (~1 fl) which is defined by the Point Spread Function (PSF) (Fig 1a). This function is the result of the microscope focused optical system convolution with the point source emission of the fluorophore and is therefore characteristic of the experimental setup and fluorophore. The detected fluorescence intensity as a function of time is defined as: ( ) = ( ) ( , ), (1) where k is the detector's sensitivity, Q is the fluorescence quantum yield, W(r) describes the illumination profile and C(r, t) is a function of the fluorophore concentration over time. In the case of single-photon confocal microscopy, the illumination profile W(r) follows a Gaussian distribution whereas for two-photon excitation, W(r) is polynomial, i.e. Gaussian-Lorentzian. In order to perform FCS tens of millions of measurements must be acquired at high frequency, generally in the kHz to MHz range. Fluctuations around the mean value ( ) contain information regarding the particles' diffusive nature (Fig. 1b)  ( ) = ( ) ( ) (2) The correlation between ( ) and ( + ) is calculated for a range of delay times. The resulting autocorrelation function G() represents the self-similarity of the signal (Fig. 1c). The autocorrelation function of the fluorescence fluctuations is defined as  : ( ) = ( ) ( ) ( ) , (3) where time t refers to the time point of intensity acquisition, to the time delay between acquisitions and indicates average. The autocorrelation function contains information on the molecular diffusion coefficient and the number of molecules occupying the observation volume. To interpret such data in molecular terms we need a model to describe the fluctuations. An example is the model of free diffusion in three dimensions, which is defined as : ( ) = (0) 1 + 1 + / , with = , (4) where is the diffusion time, s is the radius and u is the half-length of the observation volume. The parameter is usually expressed as = , with as the eccentricity of the observation volume, which typically has a radius of 0.25 and a half-length of 1.0 . In the simplest case, two parameters define the autocorrelation function: the amplitude of the fluctuation when tends to 0 ( ( )), and the characteristic relaxation time of the fluctuations. The amplitude of the autocorrelation function ( ) is proportional to the number of molecules , by / (0) where is a geometric factor that depends on the illumination profile. For a Gaussian volume =1 8 0.35 , whereas for a Gaussian-Lorentzian volume 0.076. The decay of the autocorrelation curve is directly proportional to the diffusion coefficient (length2 time-1) (Fig. 1e).
Microscopy and imaging science: practical approaches to applied research and education (A. Mndez-Vilas