Numerical fluorescence correlation spectroscopy for the analysis of molecular dynamics under nonstandard conditions

Current capabilities and future perspectives of FCS: super-resolution microscopy, machine learning, and in vivo applications

Fluorescence correlation spectroscopy (FCS) is a single molecule sensitive tool for the quantitative measurement of biomolecular dynamics and interactions. Improvements in biology, computation, and detection technology enable real-time FCS experiments with multiplexed detection even in vivo. These new imaging modalities of FCS generate data at the rate of hundreds of MB/s requiring efficient data processing tools to extract information. Here, we briefly review FCS's capabilities and limitations before discussing recent directions that address these limitations with a focus on imaging modalities of FCS, their combinations with super-resolution microscopy, new evaluation strategies, especially machine learning, and applications in vivo.

Fluorescence strategies for mapping cell membrane dynamics and structures

Fluorescence spectroscopy has been a cornerstone of research in membrane dynamics and organization. Technological advances in fluorescence spectroscopy went hand in hand with discovery of various physicochemical properties of membranes at nanometric spatial and microsecond timescales. In this perspective, we discuss the various challenges associated with quantification of physicochemical properties of membranes and how various modes of fluorescence spectroscopy have overcome these challenges to shed light on the structure and organization of membranes. Finally, we discuss newer measurement strategies and data analysis tools to investigate the structure, dynamics, and organization of membranes.

Biological noise abatement: coordinating the responses of autonomous bacteria in a synthetic biofilm to a fluctuating environment using a stochastic bistable switch

Noise is inherent to single cell behavior. Its origins can be traced to the stochasticity associated with a few copies of genes and low concentrations of protein and ligands. We have studied the mechanisms by which the response of noisy elements can be entrained for biological signal processing. To elicit predictable biological function, we have engineered a gene environment that incorporates a gene regulatory network with the stringently controlled microenvironment found in a synthetic biofilm. The regulatory network leverages the positive feedback found in quorum-sensing regulatory components of the lux operon, which is used to coordinate cellular responses to environmental fluctuations. Accumulation of the Lux receptor in cells, resulting from autoregulation, confers a rapid response and enhanced sensitivity to the quorum-sensing molecule that is retained after cell division as epigenetic memory. The memory of the system channels stochastic noise into a coordinated response among quorum-sensing signal receivers in a synthetic biofilm in which the noise diminishes with repeated exposure to noisy transmitters on the input of a signaling cascade integrated into the same biofilm. Thus, gene expression in the receivers, which are autonomous and do not communicate with each other, is synchronized to fluctuations in the environment.

The performance of 2D array detectors for light sheet based fluorescence correlation spectroscopy

Single plane illumination microscopy based fluorescence correlation spectroscopy (SPIM-FCS) is a new method for imaging FCS in 3D samples, providing diffusion coefficients, transport, flow velocities and concentrations in an imaging mode. SPIM-FCS records correlation functions over a whole plane in a sample, which requires array detectors for recording the fluorescence signal. Several types of image sensors are suitable for FCS. They differ in properties such as effective area per pixel, quantum efficiency, noise level and read-out speed. Here we compare the performance of several low light array detectors based on three different technologies: (1) Single-photon avalanche diode (SPAD) arrays, (2) passive-pixel electron multiplying charge coupled device (EMCCD) and (3) active-pixel scientific-grade complementary metal oxide semiconductor cameras (sCMOS). We discuss the influence of the detector characteristics on the effective FCS observation volume, and demonstrate that light sheet based SPIM-FCS provides absolute diffusion coefficients. This is verified by parallel measurements with confocal FCS, single particle tracking (SPT), and the determination of concentration gradients in space and time. While EMCCD cameras have a temporal resolution in the millisecond range, sCMOS cameras and SPAD arrays can extend the time resolution of SPIM-FCS down to 10 μs or lower.

Bayesian approach to the analysis of fluorescence correlation spectroscopy data II: application to simulated and in vitro data

Fluorescence correlation spectroscopy (FCS) is a powerful approach to characterizing the binding and transport dynamics of macromolecules. The unbiased interpretation of FCS data relies on the evaluation of multiple competing hypotheses to describe an underlying physical process under study, which is typically unknown a priori. Bayesian inference provides a convenient framework for this evaluation based on the temporal autocorrelation function (TACF), as previously shown theoretically using model TACF curves (He, J., Guo, S., and Bathe, M. Anal. Chem. 2012, 84). Here, we apply this procedure to simulated and experimentally measured photon-count traces analyzed using a multitau correlator, which results in complex noise properties in TACF curves that cannot be modeled easily. As a critical component of our technique, we develop two means of estimating the noise in TACF curves based either on multiple independent TACF curves themselves or a single raw underlying intensity trace, including a general procedure to ensure that independent, uncorrelated samples are used in the latter approach. Using these noise definitions, we demonstrate that the Bayesian approach selects the simplest hypothesis that describes the FCS data based on sampling and signal limitations, naturally avoiding overfitting. Further, we show that model probabilities computed using the Bayesian approach provide a reliability test for the downstream interpretation of model parameter values estimated from FCS data. Our procedure is generally applicable to FCS and image correlation spectroscopy and therefore provides an important advance in the application of these methods to the quantitative biophysical investigation of complex analytical and biological systems.

FRET fluctuation spectroscopy of diffusing biopolymers: contributions of conformational dynamics and translational diffusion

The use of fluorescence correlation spectroscopy (FCS) to study conformational dynamics in diffusing biopolymers requires that the contributions to the signal due to translational diffusion are separated from those due to conformational dynamics. A simple approach that has been proposed to achieve this goal involves the analysis of fluctuations in fluorescence resonance energy transfer (FRET) efficiency. In this work, we investigate the applicability of this methodology by combining Monte Carlo simulations and experiments. Results show that diffusion does not contribute to the measured fluctuations in FRET efficiency in conditions where the relaxation time of the kinetic process is much shorter than the mean transit time of the molecules in the optical observation volume. However, in contrast to what has been suggested in previous work, the contributions of diffusion are otherwise significant. Neglecting the contributions of diffusion can potentially lead to an erroneous interpretation of the kinetic mechanisms. As an example, we demonstrate that the analysis of FRET fluctuations in terms of a purely kinetic model would generally lead to the conclusion that the system presents complex kinetic behavior even for an idealized two-state system.

Fluorescence correlation spectroscopy: criteria for analysis in complex systems

We have evaluated the effect of varying three key parameters for Fluorescence Correlation Spectroscopy analysis, first in the context of a one species/one environment system, and then in a complex system composed of two species, or conversely, two environments. We establish experimentally appropriate settings for the (1) minimum lag time, (2) maximum lag time, and (3) averaging times over which an autocorrelation is carried out, as a function of expected diffusion decay time for a particular solute, and show that use of appropriate settings plays a critical role in recovering accurate and reliable decay times and resulting diffusion constants. Both experimental and simulated data were used to show that for a complex binary system, to extract accurate diffusion constants for both species, decay times must be bounded by adequate minimum and maximum lag times as dictated by the fast and slow diffusing species, respectively. We also demonstrate that even when constraints on experimental conditions do not permit achieving the necessary lag time limits for both of the species in a binary system, the accuracy of the recovered diffusion constant for the one species whose autocorrelation function is fully time-resolved is unaffected by uncertainty in fitting introduced by the presence of the second species.