Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Many proteins fulfill their function in dynamic complexes with other molecules, mediated by conformational changes and transient associations on a broad range of timescales^1,2,3. Coupled to an external energy source (e.g., ATP) these dynamic interactions can lead to directionality in a functional cycle and ultimately maintain the non-equilibrium steady-state in a cell, the prerequisite for life.

In order to fully understand these molecular machines, a static description guided by structural studies is not sufficient. In addition, it is essential to have knowledge of the underlying kinetic model and to determine the kinetic rate constants. Several existing methods allow researchers to study the dynamics of binary interactions between two molecules of interest, e.g., surface plasmon resonance, relaxation methods with a spectroscopic readout (e.g., jump or stopped-flow techniques), and nuclear magnetic resonance. However, their applicability is in most cases limited to simple two-state systems (e.g., one bound and one unbound state) due to the averaging inherent to bulk experiments. In cases where more states or intermediates are involved, they yield only a complex mixture of the rate constants. Single-molecule methods such as optical or magnetic tweezers or two-color smFRET, i.e., one donor and one acceptor fluorophore, with a surface-immobilized sample can recover the rate constants for all observed conformational changes. However, when it comes to interactions affecting more than one binding site, these methods remain limited and the information on the possible correlation of the two (or more) interactions will only be accessible via indirect conclusions from a set of experiments.

Multi-color smFRET^4,5,6,7,8,9 offers the opportunity to study the interaction between these components directly, at real time and under near-physiological conditions¹⁰. This permits one to investigate for example, the conformation-dependent binding of a ligand or another protein^8,9,11. The overall approach presented here is to label the protein(s) of interest at specific positions, to attach one protein to the surface of the measurement chamber, and to track the fluorescence intensity over time on a prism-type TIRFM (for details see ^9,12). The spatial proximity of the different dyes can then be determined from the energy transfer between them. Labeling strategies may vary from protein to protein (reviewed in ¹³) and guidelines to avoid artifacts in smFRET measurements exist¹⁴.

Since a donor dye may transfer energy to different acceptor dyes in a multi-color smFRET experiment, the relative position of all dyes is not accessible from excitation of one dye alone^15,16. But in combination with alternating laser excitation (ALEX¹⁷, and reviewed in ¹⁸) this method provides all spatio-temporal information at sub-second and sub-nanometer resolution.

In principal, high resolution structural information can be achieved by using the inter-dye distances calculated from the combination of all fluorescence intensities in a multi-color smFRET experiment with ALEX. However, here we focus on state identification and separation as well as the extraction of kinetic models, where multi-color smFRET is indispensable. When "only" structure determination by triangulation is desired, a set of simpler two-color smFRET experiments with high signal-to-noise ratio can be performed^12,19.

We use the partial fluorescence () as a proxy for the energy transfer between two fluorophores⁷. The PF is calculated from the fluorescence intensity analogous to the FRET efficiency of a two-color experiment:

Where, is the intensity in emission channel em after excitation with color ex, and c is the acceptor with the longest wavelength. Detection channels represent the same position in the sample chamber but record different spectral ranges of the fluorescence light. The same identifier for excitation and emission are used in this protocol (i.e., "blue," "green," and "red").

Because of experimental shortcomings the measured fluorescence intensities depend not only on the energy transfer but also on fluorophore and setup properties. In order to obtain the true energy transfer efficiency between two fluorophores, the measured intensities have to be corrected. The following procedure is based on reference⁹. Correction factors for apparent leakage (lk, i.e., the detection of photons from a fluorophore in a channel designated for another dye) and apparent gamma (ag, i.e., the fluorescence quantum yield of the dye and the detection efficiency of the channel) are obtained from single-molecule traces that show an acceptor bleaching event.

The leakage of the donor dye into every possible acceptor channel is calculated from all data points in the recorded fluorescence traces where the acceptor dye bleached but the donor is still fluorescent ():

The median of the leakage histogram is used as the apparent leakage factor. After correction for leakage, the apparent gamma factor is determined from the same set of traces. It is calculated by dividing the change of fluorescence in the acceptor channel by the change of fluorescence in the donor channel upon bleaching of the acceptor dye:

Where c again is the detection channel for the acceptor with the longest wavelength. The median of the resulting distribution is used as the apparent correction factor.

The corrected intensities in each channel are obtained by:

The PF is then calculated according to:

Different populations can be separated in the multi-dimensional space spanned by the PFs. The position and width of each state is determined by fitting the data with multi-dimensional Gaussian functions. Subsequent optimization of one global HMM based on all PF traces provides a quantitative description of the observed kinetics. Even small changes of the rates are detectable.

HMMs provide a way of inferring a state model from a collection of noisy time traces. The system is considered to be in one of a set of discrete, hidden states at any given time and the actual observation (i.e., the emission) is a probabilistic function of this hidden state²⁰. In the case of TIRFM smFRET data, the emission probabilities b_i per state i can be modeled by continuous Gaussian probability density functions. At regularly spaced discrete time points, transitions from one to another state can occur according to the transition probability that is time-invariant and only depends on the current state. The transition matrix A contains these transition probabilities a_ij between all hidden states. The initial state distribution gives the state-specific probabilities for the first time point of a time trace. Using a maximum-likelihood approach, these parameters can be optimized to best describe the data with the Forward-Backward and Baum-Welch algorithms^20,21. This yields the maximum likelihood estimators (MLE). Finally, the state sequence that most likely produced the trajectory of observations can be inferred with the Viterbi algorithm. In contrast to other HMM analyses of smFRET data^24,25,26 we do not use the HMM as a mere "smoothing" of the data but extract the kinetic state model from the data set without the need for fitting dwell time histograms²⁷. HMM analysis is done with in-house scripts using Igor Pro. Implementation of the code is based on reference²¹. We provide a software kit and exemplary data on our webpage in order to follow sections 5 and 6 of this protocol (https://www.singlemolecule.uni-freiburg.de/software/3d-fret). Full software is available upon request.

Time points in the data with PF <-1 or PF >2 in any detection channel are assigned the minimal emission probability for all states (10^-200). This prevents artificial transitions at these data points.

The parameters for the emission probabilities are obtained from the fit of the 3D PF histogram with Gaussian functions as described in step 5.7. These parameters are kept fixed during the optimization of the HMM.

In the presented approach, the initial state distribution vector and the transition matrix are used globally to describe the entire ensemble of traces. They are updated based on all N molecules from the data set according to reference²⁷.

Start parameters for the initial state distribution are determined from 2D projections of the PF histogram (step 5.3) and the transition probabilities are set to 0.05 with the exception of the probabilities to stay in the same state, which are chosen such that the probability to leave a certain state is normalized to unity.

A likelihood profiling method is used to give confidence intervals (CIs) for all transition rates^21,22, which serve as meaningful estimates for their uncertainty. To calculate the bounds of the CI for a specific rate, the transition probability of interest is fixed to a value other than the MLE. This yields the test model λ'. A likelihood ratio (LR) test of the likelihood given the data set 0 is performed according to:

The 95% confidence bound for the parameter is reached when LR exceeds 3.841, the 95% quantile of a x²-distribution with one degree of freedom^22,23.

The power of the method is demonstrated using the Hsp90. This abundant protein is found in bacteria and eukaryotes and is part of the cellular stress response²⁸. It is a promising drug target in cancer treatment²⁹. Hsp90 is a homodimer with one nucleotide binding pocket in the N-terminal domain of each subunit³⁰. It can undergo transitions between at least two globally distinct conformations, one closed and one N-terminal open, V-shaped conformation^19,31,32. The dimeric nature directly raises the question of the interplay between the two nucleotide binding sites in Hsp90.

In the following, we provide a step-by-step protocol for the data acquisition and analysis of a three-color smFRET experiment on yeast Hsp90 and nucleotide. The conformation-dependent binding of fluorescently labeled AMP-PNP (AMP-PNP*, a non-hydrolyzable analog of ATP) is analyzed. The application of the described procedure permits the study of the nucleotide binding and at the same time the conformational changes of Hsp90 and thereby reveals the cooperativity between the two nucleotide binding pockets of Hsp90.