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1.  A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli 
Combining in vivo FRET with time-varying stimuli, such as steps, ramps, and sinusoids allowed deduction of the molecular mechanisms underlying cellular signal processing.The bacterial chemotaxis pathway can be described as a two-module feedback circuit, the transfer functions of which we have characterized quantitatively by experiment. Model-driven experimental design allowed the use of a single FRET pair for measurements of both transfer functions of the pathway.The adaptation module's transfer function revealed that feedback near steady state is weak, consistent with high sensitivity to shallow gradients, but also strong steady-state fluctuations in pathway output.The measured response to oscillatory stimuli defines the frequency band over which the chemotaxis system can compute time derivatives.
In searching for better environments, bacteria sample their surroundings by random motility, and make temporal comparisons of experienced sensory cues to bias their movement toward favorable directions (Berg and Brown, 1972). Thus, the problem of sensing spatial gradients is reduced to time-derivative computations, carried out by a signaling pathway that is well characterized at the molecular level in Escherichia coli. Here, we study the physiology of this signal processing system in vivo by fluorescence resonance energy transfer (FRET) experiments in which live cells are stimulated by time-varying chemoeffector signals. By measuring FRET between the active response regulator of the pathway CheY-P and its phosphatase CheZ, each labeled with GFP variants, we obtain a readout that is directly proportional to pathway activity (Sourjik et al, 2007). We analyze the measured response functions in terms of mechanistic models of signaling, and discuss functional consequences of the observed quantitative characteristics.
Experiments are guided by a coarse-grained modular model (Tu et al, 2008) of the sensory network (Figure 1), in which we identify two important ‘transfer functions': one corresponding to the receptor–kinase complex, which responds to changes in input ligand concentration on a fast time scale, and another corresponding to the adaptation system, which provides negative feedback, opposing the effect of ligand on a slower time scale. For the receptor module, we calibrate an allosteric MWC-type model of the receptor–kinase complex by FRET measurements of the ‘open-loop' transfer function G([L],m) using step stimuli. This calibration provides a basis for using the same FRET readout (between CheY-P and CheZ) to further study properties of the adaptation module.
It is well known that adaptation in E. coli's chemotaxis system uses integral feedback, which guarantees exact restoration of the baseline activity after transient responses to step stimuli (Barkai and Leibler, 1997; Yi et al, 2000). However, the output of time-derivative computations during smoothly varying stimuli depends not only on the presence of integral feedback, but also on what is being integrated. As this integrand can in general be any function of the output, we represent it by a black-box function F(a) in our model, and set out to determine its shape by experiments with time-varying stimuli.
We first apply exponential ramp stimuli—waveforms in which the logarithm of the stimulus level varies linearly with time, at a fixed rate r. It was shown many years ago that during such a stimulus, the kinase output of the pathway changes to a new constant value, ac that is dependent on the applied ramp rate, r (Block et al, 1983). A plot of ac versus r (Figure 5A) can thus be considered as an output of time-derivative computations by the network, and could also be used to study the ‘gradient sensitivity' of bacteria traveling at constant speeds.
To obtain the feedback transfer function, F(a), we apply a simple coordinate transformation, identified using our model, to the same ramp-response data (Figure 5B). This function reveals how the temporal rate of change of the feedback signal m depends on the current output signal a. The shape of this function is analyzed using a biochemical reaction scheme, from which in vivo kinetic parameters of the feedback enzymes, CheR and CheB, are extracted. The fitted Michaelis constants for these enzymatic reactions are small compared with the steady-state abundance of their substrates, thus indicating that these enzymes operate close to saturation in vivo. The slope of the function near steady state can be used to assess the strength of feedback, and to compute the relaxation time of the system, τm. Relaxation is found to be slow (i.e. large τm), consistent with large fluctuations about the steady-state activity caused by the near-saturation kinetics of the feedback enzymes (Emonet and Cluzel, 2008).
Finally, exponential sine-wave stimuli are used to map out the system's frequency response (Figure 5C). The measured data points for both the amplitude and phase of the response are found to be in excellent agreement with model predictions based on parameters from the independently measured step and ramp responses. No curve fitting was required to obtain this agreement. Although the amplitude response as a function of frequency resembles a first-order high-pass filter with a well-defined cutoff frequency, νm, we point out that the chemotaxis pathway is actually a low-pass filter if the time derivative of the input is viewed as the input signal. In this latter perspective, νm defines an upper bound for the frequency band over which time-derivative computations can be carried out.
The two types of measurements yield complementary information regarding time-derivative computations by E. coli. The ramp-responses characterize the asymptotically constant output when a temporal gradient is held fixed over extended periods. Interestingly, the ramp responses do not depend on receptor cooperativity, but only on properties of the adaptation system, and thus can be used to reveal the in vivo adaptation kinetics, even outside the linear regime of the kinase response. The frequency response is highly relevant in considering spatial searches in the real world, in which experienced gradients are not held fixed in time. The characteristic cutoff frequency νm is found by working within the linear regime of the kinase response, and depends on parameters from both modules (it increases with both cooperativity in the receptor module, and the strength of feedback in the adaptation module).
Both ramp responses and sine-wave responses were measured at two different temperatures (22 and 32°C), and found to differ significantly. Both the slope of F(a) near steady state, from ramp experiments, and the characteristic cutoff frequency, from sine-wave experiments, were higher by a factor of ∼3 at 32°C. Fits of the enzymatic model to F(a) suggest that temperature affects the maximal velocity (Vmax) more strongly than the Michaelis constants (Km) for CheR and CheB.
Successful application of inter-molecular FRET in live cells using GFP variants always requires some degree of serendipity. Genetic fusions to these bulky fluorophores can impair the function of the original proteins, and even when fusions are functional, efficient FRET still requires the fused fluorophores to come within the small (<10 nm) Förster radius on interactions between the labeled proteins. Thus, when a successful FRET pair is identified, it is desirable to make the most of it. We have shown here that combined with careful temporal control of input stimuli, and appropriately calibrated models, a single FRET pair can be used to study the structure of multiple transfer functions within a signaling network.
The Escherichia coli chemotaxis-signaling pathway computes time derivatives of chemoeffector concentrations. This network features modules for signal reception/amplification and robust adaptation, with sensing of chemoeffector gradients determined by the way in which these modules are coupled in vivo. We characterized these modules and their coupling by using fluorescence resonance energy transfer to measure intracellular responses to time-varying stimuli. Receptor sensitivity was characterized by step stimuli, the gradient sensitivity by exponential ramp stimuli, and the frequency response by exponential sine-wave stimuli. Analysis of these data revealed the structure of the feedback transfer function linking the amplification and adaptation modules. Feedback near steady state was found to be weak, consistent with strong fluctuations and slow recovery from small perturbations. Gradient sensitivity and frequency response both depended strongly on temperature. We found that time derivatives can be computed by the chemotaxis system for input frequencies below 0.006 Hz at 22°C and below 0.018 Hz at 32°C. Our results show how dynamic input–output measurements, time honored in physiology, can serve as powerful tools in deciphering cell-signaling mechanisms.
doi:10.1038/msb.2010.37
PMCID: PMC2913400  PMID: 20571531
adaptation; feedback; fluorescence resonance energy transfer (FRET); frequency response; Monod–Wyman–Changeux (MWC) model
2.  Anomalous Surplus Energy Transfer Observed with Multiple FRET Acceptors 
PLoS ONE  2009;4(11):e8031.
Background
Förster resonance energy transfer (FRET) is a mechanism where energy is transferred from an excited donor fluorophore to adjacent chromophores via non-radiative dipole-dipole interactions. FRET theory primarily considers the interactions of a single donor-acceptor pair. Unfortunately, it is rarely known if only a single acceptor is present in a molecular complex. Thus, the use of FRET as a tool for measuring protein-protein interactions inside living cells requires an understanding of how FRET changes with multiple acceptors. When multiple FRET acceptors are present it is assumed that a quantum of energy is either released from the donor, or transferred in toto to only one of the acceptors present. The rate of energy transfer between the donor and a specific acceptor (kD→A) can be measured in the absence of other acceptors, and these individual FRET transfer rates can be used to predict the ensemble FRET efficiency using a simple kinetic model where the sum of all FRET transfer rates is divided by the sum of all radiative and non-radiative transfer rates.
Methodology/Principal Findings
The generality of this approach was tested by measuring the ensemble FRET efficiency in two constructs, each containing a single fluorescent-protein donor (Cerulean) and either two or three FRET acceptors (Venus). FRET transfer rates between individual donor-acceptor pairs within these constructs were calculated from FRET efficiencies measured after systematically introducing point mutations to eliminate all other acceptors. We find that the amount of energy transfer observed in constructs having multiple acceptors is significantly greater than the FRET efficiency predicted from the sum of the individual donor to acceptor transfer rates.
Conclusions/Significance
We conclude that either an additional energy transfer pathway exists when multiple acceptors are present, or that a theoretical assumption on which the kinetic model prediction is based is incorrect.
doi:10.1371/journal.pone.0008031
PMCID: PMC2778011  PMID: 19946626
3.  Internal Calibration Förster Resonance Energy Transfer Assay: A Real-Time Approach for Determining Protease Kinetics 
Sensors (Basel, Switzerland)  2013;13(4):4553-4570.
Förster resonance energy transfer (FRET) technology has been widely used in biological and biomedical research. This powerful tool can elucidate protein interactions in either a dynamic or steady state. We recently developed a series of FRET-based technologies to determine protein interaction dissociation constant and for use in high-throughput screening assays of SUMOylation. SUMO (small ubiquitin-like modifier) is conjugated to substrates through an enzymatic cascade. This important posttranslational protein modification is critical for multiple biological processes. Sentrin/SUMO-specific proteases (SENPs) act as endopeptidases to process the pre-SUMO or as isopeptidases to deconjugate SUMO from its substrate. Here, we describe a novel quantitative FRET-based protease assay for determining the kinetics of SENP1. Our strategy is based on the quantitative analysis and differentiation of fluorescent emission signals at the FRET acceptor emission wavelengths. Those fluorescent emission signals consist of three components: the FRET signal and the fluorescent emissions of donor (CyPet) and acceptor (YPet). Unlike our previous method in which donor and acceptor direct emissions were excluded by standard curves, the three fluorescent emissions were determined quantitatively during the SENP digestion process from onesample. New mathematical algorithms were developed to determine digested substrate concentrations directly from the FRET signal and donor/acceptor direct emissions. The kinetic parameters, kcat, KM, and catalytic efficiency (kcat/KM) of SENP1 catalytic domain for pre-SUMO1/2/3 were derived. Importantly, the general principles of this new quantitative methodology of FRET-based protease kinetic determinations can be applied to other proteases in a robust and systems biology approach.
doi:10.3390/s130404553
PMCID: PMC3673099  PMID: 23567524
quantitative FRET analysis; internal calibration; one-sample assay; protease kinetics; SENP
4.  Rapid Global Fitting of Large Fluorescence Lifetime Imaging Microscopy Datasets 
PLoS ONE  2013;8(8):e70687.
Fluorescence lifetime imaging (FLIM) is widely applied to obtain quantitative information from fluorescence signals, particularly using Förster Resonant Energy Transfer (FRET) measurements to map, for example, protein-protein interactions. Extracting FRET efficiencies or population fractions typically entails fitting data to complex fluorescence decay models but such experiments are frequently photon constrained, particularly for live cell or in vivo imaging, and this leads to unacceptable errors when analysing data on a pixel-wise basis. Lifetimes and population fractions may, however, be more robustly extracted using global analysis to simultaneously fit the fluorescence decay data of all pixels in an image or dataset to a multi-exponential model under the assumption that the lifetime components are invariant across the image (dataset). This approach is often considered to be prohibitively slow and/or computationally expensive but we present here a computationally efficient global analysis algorithm for the analysis of time-correlated single photon counting (TCSPC) or time-gated FLIM data based on variable projection. It makes efficient use of both computer processor and memory resources, requiring less than a minute to analyse time series and multiwell plate datasets with hundreds of FLIM images on standard personal computers. This lifetime analysis takes account of repetitive excitation, including fluorescence photons excited by earlier pulses contributing to the fit, and is able to accommodate time-varying backgrounds and instrument response functions. We demonstrate that this global approach allows us to readily fit time-resolved fluorescence data to complex models including a four-exponential model of a FRET system, for which the FRET efficiencies of the two species of a bi-exponential donor are linked, and polarisation-resolved lifetime data, where a fluorescence intensity and bi-exponential anisotropy decay model is applied to the analysis of live cell homo-FRET data. A software package implementing this algorithm, FLIMfit, is available under an open source licence through the Open Microscopy Environment.
doi:10.1371/journal.pone.0070687
PMCID: PMC3734241  PMID: 23940626
5.  Assessing FRET using Spectral Techniques 
Förster resonance energy transfer (FRET) techniques have proven invaluable for probing the complex nature of protein–protein interactions, protein folding, and intracellular signaling events. These techniques have traditionally been implemented with the use of one or more fluorescence band-pass filters, either as fluorescence microscopy filter cubes, or as dichroic mirrors and band-pass filters in flow cytometry. In addition, new approaches for measuring FRET, such as fluorescence lifetime and acceptor photobleaching, have been developed. Hyperspectral techniques for imaging and flow cytometry have also shown to be promising for performing FRET measurements. In this study, we have compared traditional (filter-based) FRET approaches to three spectral-based approaches: the ratio of acceptor-to-donor peak emission, linear spectral unmixing, and linear spectral unmixing with a correction for direct acceptor excitation. All methods are estimates of FRET efficiency, except for one-filter set and three-filter set FRET indices, which are included for consistency with prior literature. In the first part of this study, spectrofluorimetric data were collected from a CFP–Epac–YFP FRET probe that has been used for intracellular cAMP measurements. All comparisons were performed using the same spectrofluorimetric datasets as input data, to provide a relevant comparison. Linear spectral unmixing resulted in measurements with the lowest coefficient of variation (0.10) as well as accurate fits using the Hill equation. FRET efficiency methods produced coefficients of variation of less than 0.20, while FRET indices produced coefficients of variation greater than 8.00. These results demonstrate that spectral FRET measurements provide improved response over standard, filter-based measurements. Using spectral approaches, single-cell measurements were conducted through hyperspectral confocal microscopy, linear unmixing, and cell segmentation with quantitative image analysis. Results from these studies confirmed that spectral imaging is effective for measuring subcellular, time-dependent FRET dynamics and that additional fluorescent signals can be readily separated from FRET signals, enabling multilabel studies of molecular interactions.
doi:10.1002/cyto.a.22340
PMCID: PMC4374658  PMID: 23929684
CFP; YFP; Epac; cAMP; spectroscopy; hyperspectral; microscopy; imaging; flow cytometry
6.  The Interaction Affinity between Vascular Cell Adhesion Molecule-1 (VCAM-1) and Very Late Antigen-4 (VLA-4) Analyzed by Quantitative FRET 
PLoS ONE  2015;10(3):e0121399.
Very late antigen-4 (VLA-4), a member of integrin superfamily, interacts with its major counter ligand vascular cell adhesion molecule-1 (VCAM-1) and plays an important role in leukocyte adhesion to vascular endothelium and immunological synapse formation. However, irregular expressions of these proteins may also lead to several autoimmune diseases and metastasis cancer. Thus, quantifying the interaction affinity of the VCAM-1/VLA-4 interaction is of fundamental importance in further understanding the nature of this interaction and drug discovery. In this study, we report an ‘in solution’ steady state organic fluorophore based quantitative fluorescence resonance energy transfer (FRET) assay to quantify this interaction in terms of the dissociation constant (Kd). We have used, in our FRET assay, the Alexa Fluor 488-VLA-4 conjugate as the donor, and Alexa Fluor 546-VCAM-1 as the acceptor. From the FRET signal analysis, Kd of this interaction was determined to be 41.82 ± 2.36 nM. To further confirm our estimation, we have employed surface plasmon resonance (SPR) technique to obtain Kd = 39.60 ± 1.78 nM, which is in good agreement with the result obtained by FRET. This is the first reported work which applies organic fluorophore based ‘in solution’ simple quantitative FRET assay to obtain the dissociation constant of the VCAM-1/VLA-4 interaction, and is also the first quantification of this interaction. Moreover, the value of Kd can serve as an indicator of abnormal protein-protein interactions; hence, this assay can potentially be further developed into a drug screening platform of VLA-4/VCAM-1 as well as other protein-ligand interactions.
doi:10.1371/journal.pone.0121399
PMCID: PMC4368157  PMID: 25793408
7.  Structural Heterogeneity and Quantitative FRET Efficiency Distributions of Polyprolines through a Hybrid Atomistic Simulation and Monte Carlo Approach 
PLoS ONE  2011;6(5):e19791.
Förster Resonance Energy Transfer (FRET) experiments probe molecular distances via distance dependent energy transfer from an excited donor dye to an acceptor dye. Single molecule experiments not only probe average distances, but also distance distributions or even fluctuations, and thus provide a powerful tool to study biomolecular structure and dynamics. However, the measured energy transfer efficiency depends not only on the distance between the dyes, but also on their mutual orientation, which is typically inaccessible to experiments. Thus, assumptions on the orientation distributions and averages are usually made, limiting the accuracy of the distance distributions extracted from FRET experiments. Here, we demonstrate that by combining single molecule FRET experiments with the mutual dye orientation statistics obtained from Molecular Dynamics (MD) simulations, improved estimates of distances and distributions are obtained. From the simulated time-dependent mutual orientations, FRET efficiencies are calculated and the full statistics of individual photon absorption, energy transfer, and photon emission events is obtained from subsequent Monte Carlo (MC) simulations of the FRET kinetics. All recorded emission events are collected to bursts from which efficiency distributions are calculated in close resemblance to the actual FRET experiment, taking shot noise fully into account. Using polyproline chains with attached Alexa 488 and Alexa 594 dyes as a test system, we demonstrate the feasibility of this approach by direct comparison to experimental data. We identified cis-isomers and different static local environments as sources of the experimentally observed heterogeneity. Reconstructions of distance distributions from experimental data at different levels of theory demonstrate how the respective underlying assumptions and approximations affect the obtained accuracy. Our results show that dye fluctuations obtained from MD simulations, combined with MC single photon kinetics, provide a versatile tool to improve the accuracy of distance distributions that can be extracted from measured single molecule FRET efficiencies.
doi:10.1371/journal.pone.0019791
PMCID: PMC3101224  PMID: 21629703
8.  Analysis of Complex Single Molecule FRET Time Trajectories 
Methods in enzymology  2010;472:153-178.
Single molecule methods have given researchers the ability to investigate the structural dynamics of biomolecules at unprecedented resolution and sensitivity. One of the preferred methods of studying single biomolecules is single-molecule fluorescence resonance energy transfer (smFRET). The popularity of smFRET stems from its ability to report on dynamic, either intra- or intermolecular interactions in real-time. For example, smFRET has been successfully used to characterize the role of dynamics in functional RNAs and their protein complexes, including ribozymes, the ribosome, and more recently the spliceosome. Being able to reliably extract quantitative kinetic and conformational parameters from smFRET experiments is crucial for the interpretation of their results. The need for efficient, unbiased analysis routines becomes more evident as the systems studied become more complex. In this article we focus on the practical utility of statistical algorithms, particularly hidden Markov models, to aid in the objective quantification of complex smFRET trajectories with three or more discrete states, and to extract kinetic information from the trajectories. Additionally, we present a method for systematically eliminating transitions associated with uncorrelated fluorophore behavior that may occur due to dye anisotropy and quenching effects. We also highlight the importance of data condensation through the use of various transition density plots to fully understand the underlying conformational dynamics and kinetic behavior of the biological macromolecule of interest under varying conditions. Finally, the application of these techniques to studies of pre-mRNA conformational changes during eukaryotic splicing is discussed.
doi:10.1016/S0076-6879(10)72011-5
PMCID: PMC3012381  PMID: 20580964
9.  Estimating the distance separating fluorescent protein FRET pairs 
Methods (San Diego, Calif.)  2013;66(2):131-138.
Förster resonance energy transfer (FRET) describes a physical phenomenon widely applied in biomedical research to estimate separations between biological molecules. Routinely, genetic engineering is used to incorporate spectral variants of the green fluorescent protein (GFPs), into cellular expressed proteins. The transfer efficiency or rate of energy transfer between donor and acceptor FPs is then assayed. As appreciable FRET occurs only when donors and acceptors are in close proximity (1–10 nm), the presence of FRET may indicate that the engineered proteins associate as interacting species. For a homogeneous population of FRET pairs the separations between FRET donors and acceptors can be estimated from a measured FRET efficiency if it is assumed that donors and acceptors are randomly oriented and rotate extensively during their excited state (dynamic regime). Unlike typical organic fluorophores, the rotational correlation-times of FPs are typically much longer than their fluorescence lifetime; accordingly FPs are virtually static during their excited state. Thus, estimating separations between FP FRET pairs is problematic. To overcome this obstacle, we present here a simple method for estimating separations between FPs using the experimentally measured average FRET efficiency. This approach assumes that donor and acceptor fluorophores are randomly oriented, but do not rotate during their excited state (static regime). This approach utilizes a Monte-Carlo simulation generated look-up table that allows one to estimate the separation, normalized to the Förster distance, from the average FRET efficiency. Assuming a dynamic regime overestimates the separation significantly (by 10% near 0.5 and 30% near 0.75 efficiencies) compared to assuming a static regime, which is more appropriate for estimates of separations between FPs.
doi:10.1016/j.ymeth.2013.06.021
PMCID: PMC3964137  PMID: 23811334
GFP; Kappa squared
10.  Improving the spectral analysis of fluorescence resonance energy transfer in live cells: Application to interferon receptors and Janus kinases 
Cytokine  2013;64(1):10.1016/j.cyto.2013.05.026.
The observed Fluorescence Resonance Energy Transfer (FRET) between fluorescently labeled proteins varies in cells. To understand how this variation affects our interpretation of how proteins interact in cells, we developed a protocol that mathematically separates donor-independent and donor-dependent excitations of acceptor, determines the electromagnetic interaction of donors and acceptors, and quantifies the efficiency of the interaction of donors and acceptors. By analyzing large populations of cells, we found that misbalanced or insufficient expression of acceptor or donor as well as their inefficient or reversible interaction influenced FRET efficiency in vivo. Use of red-shifted donors and acceptors gave spectra with less endogenous fluorescence but produced lower FRET efficiency, possibly caused by reduced quenching of red-shifted fluorophores in cells. Additionally, cryptic interactions between jellyfish FPs artefactually increased the apparent FRET efficiency. Our protocol can distinguish specific and nonspecific protein interactions even within highly constrained environments as plasma membranes. Overall, accurate FRET estimations in cells or within complex environments can be obtained by a combination of proper data analysis, study of sufficient numbers of cells, and use of properly empirically developed fluorescent proteins.
doi:10.1016/j.cyto.2013.05.026
PMCID: PMC3868223  PMID: 23796694
Interferon; FRET; Receptor; Equilibrium; Janus kinase
11.  Parallel multispot smFRET analysis using an 8-pixel SPAD array 
Proceedings of SPIE  2012;8228:10.1117/12.909470.
Single-molecule Förster resonance energy transfer (smFRET) is a powerful tool for extracting distance information between two fluorophores (a donor and acceptor dye) on a nanometer scale. This method is commonly used to monitor binding interactions or intra- and intermolecular conformations in biomolecules freely diffusing through a focal volume or immobilized on a surface. The diffusing geometry has the advantage to not interfere with the molecules and to give access to fast time scales. However, separating photon bursts from individual molecules requires low sample concentrations. This results in long acquisition time (several minutes to an hour) to obtain sufficient statistics. It also prevents studying dynamic phenomena happening on time scales larger than the burst duration and smaller than the acquisition time. Parallelization of acquisition overcomes this limit by increasing the acquisition rate using the same low concentrations required for individual molecule burst identification. In this work we present a new two-color smFRET approach using multispot excitation and detection. The donor excitation pattern is composed of 4 spots arranged in a linear pattern. The fluorescent emission of donor and acceptor dyes is then collected and refocused on two separate areas of a custom 8-pixel SPAD array. We report smFRET measurements performed on various DNA samples synthesized with various distances between the donor and acceptor fluorophores. We demonstrate that our approach provides identical FRET efficiency values to a conventional single-spot acquisition approach, but with a reduced acquisition time. Our work thus opens the way to high-throughput smFRET analysis on freely diffusing molecules.
doi:10.1117/12.909470
PMCID: PMC3874731  PMID: 24382989
single-molecule; photon counting; FRET; SPAD array; high throughput
12.  Linear Approaches to Intramolecular Förster Resonance Energy Transfer Probe Measurements for Quantitative Modeling 
PLoS ONE  2011;6(11):e27823.
Numerous unimolecular, genetically-encoded Förster Resonance Energy Transfer (FRET) probes for monitoring biochemical activities in live cells have been developed over the past decade. As these probes allow for collection of high frequency, spatially resolved data on signaling events in live cells and tissues, they are an attractive technology for obtaining data to develop quantitative, mathematical models of spatiotemporal signaling dynamics. However, to be useful for such purposes the observed FRET from such probes should be related to a biological quantity of interest through a defined mathematical relationship, which is straightforward when this relationship is linear, and can be difficult otherwise. First, we show that only in rare circumstances is the observed FRET linearly proportional to a biochemical activity. Therefore in most cases FRET measurements should only be compared either to explicitly modeled probes or to concentrations of products of the biochemical activity, but not to activities themselves. Importantly, we find that FRET measured by standard intensity-based, ratiometric methods is inherently non-linear with respect to the fraction of probes undergoing FRET. Alternatively, we find that quantifying FRET either via (1) fluorescence lifetime imaging (FLIM) or (2) ratiometric methods where the donor emission intensity is divided by the directly-excited acceptor emission intensity (denoted Ralt) is linear with respect to the fraction of probes undergoing FRET. This linearity property allows one to calculate the fraction of active probes based on the FRET measurement. Thus, our results suggest that either FLIM or ratiometric methods based on Ralt are the preferred techniques for obtaining quantitative data from FRET probe experiments for mathematical modeling purposes.
doi:10.1371/journal.pone.0027823
PMCID: PMC3218046  PMID: 22114702
13.  Quantitative multi-color FRET measurements by Fourier lifetime excitation-emission matrix spectroscopy 
Optics Express  2012;20(24):26806-26827.
Förster resonant energy transfer (FRET) is extensively used to probe macromolecular interactions and conformation changes. The established FRET lifetime analysis method measures the FRET process through its effect on the donor lifetime. In this paper we present a method that directly probes the time-resolved FRET signal with frequency domain Fourier lifetime excitation-emission matrix (FLEEM) measurements. FLEEM separates fluorescent signals by their different phonon energy pathways from excitation to emission. The FRET process generates a unique signal channel that is initiated by donor excitation but ends with acceptor emission. Time-resolved analysis of the FRET EEM channel allows direct measurements on the FRET process, unaffected by free fluorophores that might be present in the sample. Together with time-resolved analysis on non-FRET channels, i.e. donor and acceptor EEM channels, time resolved EEM analysis allows precise quantification of FRET in the presence of free fluorophores. The method is extended to three-color FRET processes, where quantification with traditional methods remains challenging because of the significantly increased complexity in the three-way FRET interactions. We demonstrate the time-resolved EEM analysis method with quantification of three-color FRET in incompletely hybridized triple-labeled DNA oligonucleotides. Quantitative measurements of the three-color FRET process in triple-labeled dsDNA are obtained in the presence of free single-labeled ssDNA and double-labeled dsDNA. The results establish a quantification method for studying multi-color FRET between multiple macromolecules in biochemical equilibrium.
doi:10.1364/OE.20.026806
PMCID: PMC3601597  PMID: 23187535
(170.6280) Spectroscopy, fluorescence and luminescence; (170.2520) Fluorescence microscopy
14.  Three-Color FRET expands the ability to quantify the interactions of several proteins involved in actin filament nucleation 
Proceedings of SPIE  2012;8226:82260J.
With traditional 2-color Förster Resonance Energy Transfer (FRET) microscopy, valuable quantitative analyses can be conducted. Correlations of donor (D), acceptor (A) and their ratios (D:A) with energy transfer efficiency (E%) or distance (r) allows measurement of changes between control and experimental samples; also, clustered vs. random assembly of cellular components can be differentiated. Essentially, only the above three parameters D, A and D:A vs. E% are the basis for these deductions. 3-color FRET uses the same basic parameters, but exponentially expands the opportunities to quantify interrelationships among 3 cellular components. We investigated a number of questions based on the results of a triple combination (F1-F2-F3) of TFP-NWASP/Venus-IQGAP1/mCherry-Actin – all involved in the nucleation of actin - to apply the extensive analysis assay possible with 3-color FRET. How do changing N-WASP or IQGAP1 fluorescence levels affect actin fluorescence? What is the effect on E% of NWASP-actin by IQGAP1 or E% of IQGAP1-actin by N-WASP? These and other questions are explored in the context of all proteins of interest being in FRET distance vs. any two in the absence of the third. 4 cases are compared based on bleed-through corrected FRET: (1) all 3 interact, (2) only F1-F3 and F2-F3 [not F1-F2], (3) only F1-F2 and F2-F3 interact [not F1-F3], (4) only F1-F2 and F1-F3 interact [not F2-F3]. Other than describing the methodology in detail, several biologically relevant results are presented showing how E% (i.e. distance), fluorescence levels and ratios are affected in each of the cases. These correlations can only be observed in a 3-fluorophore combination. 3-color FRET will greatly expand the investigative range of quantitative analysis for the life-science researcher.
doi:10.1117/12.906432
PMCID: PMC3580387  PMID: 23549657
Three-color FRET; IQGAP1; N-WASP; actin; E%; quantitative analysis; Teal; Venus; mCherry
15.  Dynamic map of protein interactions in the Escherichia coli chemotaxis pathway 
Protein–protein interactions play key roles in virtually all cellular processes, often forming complex regulatory networks. A powerful tool to study interactions in vivo is fluorescence resonance energy transfer (FRET), which is based on the distance-dependent energy transfer from an excited donor to an acceptor fluorophore. Here, we used FRET to systematically map all protein interactions in the chemotaxis signaling pathway in Escherichia coli, one of the most studied models of signal transduction, and to determine stimulation-induced changes in the pathway. Our FRET analysis identified 19 positive FRET pairs out of the 28 possible protein combinations, with 9 pairs being responsive to chemotactic stimulation. Six stimulation-dependent and five stimulation-independent interactions were direct, whereas other interactions were apparently mediated by scaffolding proteins. Characterization of stimulation-induced responses revealed an additional regulation through activity dependence of interactions involving the adaptation enzyme CheB, and showed complex rearrangement of chemosensory receptors. Our study illustrates how FRET can be efficiently employed to study dynamic protein networks in vivo.
doi:10.1038/msb.2008.77
PMCID: PMC2644175  PMID: 19156130
bacteria; chemotaxis; FRET; protein network; signal transduction
16.  Analytical use of multi-protein fluorescence resonance energy transfer to demonstrate membrane-facilitated interactions within cytokine receptor complexes 
Cytokine  2013;64(1):298-309.
Experiments measuring Fluorescence Resonance Energy Transfer (FRET) between cytokine receptor chains and their associated proteins led to hypotheses describing their organization in intact cells. These interactions occur within a larger protein complex or within a given nano-environment. To illustrate this complexity empirically, we developed a protocol to analyze FRET among more than two fluorescent proteins (multi-FRET). In multi-FRET, we model FRET among more than two fluorophores as the sum of all possible pairwise interactions within the complex. We validated our assumption by demonstrating that FRET among pairs within a fluorescent triplet resembled FRET between each pair measured in the absence of the third fluorophore. FRET between two receptor chains increases with increasing FRET between the ligand-binding chain (e.g., IFN-γR1, IL-10R1 and IFN-λR1) and an acylated fluorescent protein that preferentially resides within subsections of the plasma membrane. The interaction of IL-10R2 with IFN-λR1 or IL-10R1 results in decreased FRET between IL-10R2 and the acylated fluorescent protein. Finally, we analyzed FRET among four fluorescent proteins to demonstrate that as FRET between IFN-γR1 and IFN-γR2 or between IFN-αR1 and IFN-αR2c increases, FRET among other pairs of proteins changes within each complex.
doi:10.1016/j.cyto.2013.05.008
PMCID: PMC3770794  PMID: 23769803
FRET; Multi-protein; Interferon receptor; Lipid raft; Confocal fluorescence spectroscopy
17.  Quantitative tomographic imaging of intermolecular FRET in small animals 
Biomedical Optics Express  2012;3(12):3161-3175.
Forster resonance energy transfer (FRET) is a nonradiative transfer of energy between two fluorescent molecules (a donor and an acceptor) in nanometer range proximity. FRET imaging methods have been applied to proteomic studies and drug discovery applications based on intermolecular FRET efficiency measurements and stoichiometric measurements of FRET interaction as quantitative parameters of interest. Importantly, FRET provides information about biomolecular interactions at a molecular level, well beyond the diffraction limits of standard microscopy techniques. The application of FRET to small animal imaging will allow biomedical researchers to investigate physiological processes occurring at nanometer range in vivo as well as in situ. In this work a new method for the quantitative reconstruction of FRET measurements in small animals, incorporating a full-field tomographic acquisition system with a Monte Carlo based hierarchical reconstruction scheme, is described and validated in murine models. Our main objective is to estimate the relative concentration of two forms of donor species, i.e., a donor molecule involved in FRETing to an acceptor close by and a nonFRETing donor molecule.
doi:10.1364/BOE.3.003161
PMCID: PMC3521293  PMID: 23243567
(110.6955) Tomographic imaging; (170.6920) Time-resolved imaging; (170.3650) Lifetime-based sensing
18.  Classic Maximum Entropy Recovery of the Average Joint Distribution of Apparent FRET Efficiency and Fluorescence Photons for Single-molecule Burst Measurements 
The Journal of Physical Chemistry. B  2012;116(13):4006-4015.
We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions.
doi:10.1021/jp209861u
PMCID: PMC3320690  PMID: 22338694
Single-molecule FRET; Bayesian analysis; photon distribution analysis; maximum entropy
19.  Reconstruction of Calmodulin Single-Molecule FRET States, Dye-Interactions, and CaMKII Peptide Binding by MultiNest and Classic Maximum Entropy 
Chemical physics  2013;422:10.1016/j.chemphys.2012.11.018.
We analyze single molecule FRET burst measurements using Bayesian nested sampling. The MultiNest algorithm produces accurate FRET efficiency distributions from single-molecule data. FRET efficiency distributions recovered by MultiNest and classic maximum entropy are compared for simulated data and for calmodulin labeled at residues 44 and 117. MultiNest compares favorably with maximum entropy analysis for simulated data, judged by the Bayesian evidence. FRET efficiency distributions recovered for calmodulin labeled with two different FRET dye pairs depended on the dye pair and changed upon Ca2+ binding. We also looked at the FRET efficiency distributions of calmodulin bound to the calcium/calmodulin dependent protein kinase II (CaMKII) binding domain. For both dye pairs, the FRET efficiency distribution collapsed to a single peak in the case of calmodulin bound to the CaMKII peptide. These measurements strongly suggest that consideration of dye-protein interactions is crucial in forming an accurate picture of protein conformations from FRET data.
doi:10.1016/j.chemphys.2012.11.018
PMCID: PMC3819237  PMID: 24223465
calmodulin; FRET; single-molecule fluorescence; fluorescence dyes; Bayesian analysis; nested sampling; maximum entropy; calcium/calmodulin dependent protein kinase II
20.  Simultaneous Quantitative Live Cell Imaging of Multiple FRET-Based Biosensors 
PLoS ONE  2013;8(4):e61096.
We have developed a novel method for multi-color spectral FRET analysis which is used to study a system of three independent FRET-based molecular sensors composed of the combinations of only three fluorescent proteins. This method is made possible by a novel routine for computing the 3-D excitation/emission spectral fingerprint of FRET from reference measurements of the donor and acceptor alone. By unmixing the 3D spectrum of the FRET sample, the total relative concentrations of the fluorophores and their scaled FRET efficiencies are directly measured, from which apparent FRET efficiencies can be computed. If the FRET sample is composed of intramolecular FRET sensors it is possible to determine the total relative concentration of the sensors and then estimate absolute FRET efficiency of each sensor. Using multiple tandem constructs with fixed FRET efficiency as well as FRET-based calcium sensors with novel fluorescent protein combinations we demonstrate that the computed FRET efficiencies are accurate and changes in these quantities occur without crosstalk. We provide an example of this method’s potential by demonstrating simultaneous imaging of spatially colocalized changes in [Ca2+], [cAMP], and PKA activity.
doi:10.1371/journal.pone.0061096
PMCID: PMC3628763  PMID: 23613792
21.  Mining the Sinorhizobium meliloti Transportome to Develop FRET Biosensors for Sugars, Dicarboxylates and Cyclic Polyols 
PLoS ONE  2012;7(9):e43578.
Background
Förster resonance energy transfer (FRET) biosensors are powerful tools to detect biologically important ligands in real time. Currently FRET bisosensors are available for twenty-two compounds distributed in eight classes of chemicals (two pentoses, two hexoses, two disaccharides, four amino acids, one nucleobase, two nucleotides, six ions and three phytoestrogens). To expand the number of available FRET biosensors we used the induction profile of the Sinorhizobium meliloti transportome to systematically screen for new FRET biosensors.
Methodology/Principal Findings
Two new vectors were developed for cloning genes for solute-binding proteins (SBPs) between those encoding FRET partner fluorescent proteins. In addition to a vector with the widely used cyan and yellow fluorescent protein FRET partners, we developed a vector using orange (mOrange2) and red fluorescent protein (mKate2) FRET partners. From the sixty-nine SBPs tested, seven gave a detectable FRET signal change on binding substrate, resulting in biosensors for D-quinic acid, myo-inositol, L-rhamnose, L-fucose, β-diglucosides (cellobiose and gentiobiose), D-galactose and C4-dicarboxylates (malate, succinate, oxaloacetate and fumarate). To our knowledge, we describe the first two FRET biosensor constructs based on SBPs from Tripartite ATP-independent periplasmic (TRAP) transport systems.
Conclusions/Significance
FRET based on orange (mOrange2) and red fluorescent protein (mKate2) partners allows the use of longer wavelength light, enabling deeper penetration of samples at lower energy and increased resolution with reduced back-ground auto-fluorescence. The FRET biosensors described in this paper for four new classes of compounds; (i) cyclic polyols, (ii) L-deoxy sugars, (iii) β-linked disaccharides and (iv) C4-dicarboxylates could be developed to study metabolism in vivo.
doi:10.1371/journal.pone.0043578
PMCID: PMC3454389  PMID: 23028462
22.  Lateral Distribution of NBD-PC Fluorescent Lipid Analogs in Membranes Probed by Molecular Dynamics-Assisted Analysis of Förster Resonance Energy Transfer (FRET) and Fluorescence Quenching 
Förster resonance energy transfer (FRET) is a powerful tool used for many problems in membrane biophysics, including characterization of the lateral distribution of lipid components and other species of interest. However, quantitative analysis of FRET data with a topological model requires adequate choices for the values of several input parameters, some of which are difficult to obtain experimentally in an independent manner. For this purpose, atomistic molecular dynamics (MD) simulations can be potentially useful as they provide direct detailed information on transverse probe localization, relative probe orientation, and membrane surface area, all of which are required for analysis of FRET data. This is illustrated here for the FRET pairs involving 1,6-diphenylhexatriene (DPH) as donor and either 1-palmitoyl,2-(6-[N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino] hexanoyl)- sn-glycero-3-phosphocholine (C6-NBD-PC) or 1-palmitoyl,2-(12-[N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino]dodecanoyl)-sn-glycero-3-phosphocholine (C12-NBD-PC) as acceptors, in fluid vesicles of 1,2-dipalmitoyl-sn-3-glycerophosphocholine (DPPC, 50 °C). Incorporation of results from MD simulations improves the statistical quality of model fitting to the experimental FRET data. Furthermore, the decay of DPH in the presence of moderate amounts of C12-NBD-PC (>0.4 mol%) is consistent with non-random lateral distribution of the latter, at variance with C6-NBD-PC, for which aggregation is ruled out up to 2.5 mol% concentration. These conclusions are supported by analysis of NBD-PC fluorescence self-quenching. Implications regarding the relative utility of these probes in membrane studies are discussed.
doi:10.3390/ijms131114545
PMCID: PMC3509596  PMID: 23203080
DPH; DPPC; fluorescence; FRET; lipid bilayer; membrane probe; molecular dynamics; NBD lipid
23.  Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals 
PLoS Computational Biology  2012;8(8):e1002653.
A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.
Author Summary
Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.
doi:10.1371/journal.pcbi.1002653
PMCID: PMC3426566  PMID: 22927808
24.  Single Cell FRET Analysis for the Identification of Optimal FRET-Pairs in Bacillus subtilis Using a Prototype MEM-FLIM System 
PLoS ONE  2015;10(4):e0123239.
Protein-protein interactions can be studied in vitro, e.g. with bacterial or yeast two-hybrid systems or surface plasmon resonance. In contrast to in vitro techniques, in vivo studies of protein-protein interactions allow examination of spatial and temporal behavior of such interactions in their native environment. One approach to study protein-protein interactions in vivo is via Förster Resonance Energy Transfer (FRET). Here, FRET efficiency of selected FRET-pairs was studied at the single cell level using sensitized emission and Frequency Domain-Fluorescence Lifetime Imaging Microscopy (FD-FLIM). For FRET-FLIM, a prototype Modulated Electron-Multiplied FLIM system was used, which is, to the best of our knowledge, the first account of Frequency Domain FLIM to analyze FRET in single bacterial cells. To perform FRET-FLIM, we first determined and benchmarked the best fluorescent protein-pair for FRET in Bacillus subtilis using a novel BglBrick-compatible integration vector. We show that GFP-tagRFP is an excellent donor-acceptor pair for B. subtilis in vivo FRET studies. As a proof of concept, selected donor and acceptor fluorescent proteins were fused using a linker that contained a tobacco etch virus (TEV)-protease recognition sequence. Induction of TEV-protease results in loss of FRET efficiency and increase in fluorescence lifetime. The loss of FRET efficiency after TEV induction can be followed in time in single cells via time-lapse microscopy. This work will facilitate future studies of in vivo dynamics of protein complexes in single B. subtilis cells.
doi:10.1371/journal.pone.0123239
PMCID: PMC4401445  PMID: 25886351
25.  Assembling programmable FRET-based photonic networks using designer DNA scaffolds 
Nature Communications  2014;5:5615.
DNA demonstrates a remarkable capacity for creating designer nanostructures and devices. A growing number of these structures utilize Förster resonance energy transfer (FRET) as part of the device's functionality, readout or characterization, and, as device sophistication increases so do the concomitant FRET requirements. Here we create multi-dye FRET cascades and assess how well DNA can marshal organic dyes into nanoantennae that focus excitonic energy. We evaluate 36 increasingly complex designs including linear, bifurcated, Holliday junction, 8-arm star and dendrimers involving up to five different dyes engaging in four-consecutive FRET steps, while systematically varying fluorophore spacing by Förster distance (R0). Decreasing R0 while augmenting cross-sectional collection area with multiple donors significantly increases terminal exciton delivery efficiency within dendrimers compared with the first linear constructs. Förster modelling confirms that best results are obtained when there are multiple interacting FRET pathways rather than independent channels by which excitons travel from initial donor(s) to final acceptor.
DNA is a useful molecule with which to construct nanomaterials with controllable functionalities. Here, the authors fabricate photonic wires by appending dye molecules at set positions along DNA structures, and show how FRET performance can be tuned by modifying dye separation.
doi:10.1038/ncomms6615
PMCID: PMC4275599  PMID: 25504073

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