Maximum position of Shannon-information of FRET frequency distribution represented as a function of the a (or G) calibrating factor as calculated in the framework of dual-laser flow cytometric FRET method – also called 3-cube FRET – gives a fairly good approximation of the real a, using only a single FRET sample. The estimation is accurate for completely symmetric FRET distributions like Gaussian and uniform. For non-symmetric distributions, the committed error have been found to depend on the direction and degree of deviation from the complete symmetry. The maximum information is characterized also by zero skewness, and minima in kurtosis and in the c-value, defined as the “absolute deviation from the Gaussian”, as other a-functions characterizing shape. As to practice, information maximum of FRET distribution can be used to determine a, whenever symmetry can be assumed. In other cases, the goodness of estimation can be inferred from the information content and shape parameters (skewness, kurtosis and “c-value”) of the primarily measured FRET parameter A’, based on their inverse correlations with their counterparts computed with the target FRET distribution. Above a threshold in FRET efficiency or its coefficient of variation, resonant peaks (“W-curves”) in FRET information appear on the a-scale, with their positions stabilized around a values with reduced fluctuations dictated by symmetry of the target FRET distribution. The phenomenon is explained by a FRET-induced widening of the A’ distribution reaching the domain containing A’=-a.

Present day flow cytometers and microscopes enable combined signal detection as a function of many parameters such as the color and polarization of the exciting and emitted light, and the spatial position and orientation of the detected object, as well as the time point of the data registration [1]. Because these parameters can be changed in very fine steps, “quasi continuously,” the observations generally lead to vast amount of data sets, for example, the size of recorded movies when several physiologic parameters of a cell culture are monitored with a camera for days. The ultimate aim of basic research in molecular biology and medicine is the application of the results in diagnostics and therapies, the “translation” of the achievements of basic science to the every-day or “real life” level. Examples are the application of fluorescence polarization in cancer diagnostics [2, 3], and fluorescence lifetime for detecting various physiological parameters in the human bodies, for example, when delineating tumor boundaries during surgical intervention [4]. Huge data sets might arise here not only due to the high number of monitored parameters, but also due to the size of the monitored (scanned) areas of body surfaces. Additional complexity in these cases might arise from a need for a very quick data evaluation, preferably in parallel with the registration of the data, that is, the “real time” data processing. The collection of huge data sets with the combinatorial or hyper-dimensional microscopies, flow cytometers have been enabled by the development in the illumination and detection photonic technologies as well as the level of computerization. However, the best exploitation of this hardware level development supposes also a corresponding software-level development of very quick, robust and efficient evaluation techniques, which can also be applied sometimes “remotely,” without the touch of human hand, in a so-called “unsupervised” manner. Such methods start to become quite widespread today. They are called collectively as “artificial intelligence” techniques, referring mainly to “deep-learning,” (or “soft computing,” “machine-vision”), and “reduction of dimensionality” [5-11]. One subclass of “artificial intelligence” is “deep-learning” with its two versions called “supervised” and “unsupervised” depending on whether apriori information is available or not for the further data processing referring mainly to classification—assigning them in subgroups, “labeling”—and regression (fitting) of data. In the field of intensity ratio-based flow cytometric FRET detection, “unsupervised deep-learning” represented by the PhenoGraph technique—belonging to the “k-nearest neighbor graphing” family of methods [14]—has recently been applied by Ni et al. [15] for classification of FRET efficiency values (Figure 2). During classification or ranking, data points have been sorted into seven groups based on the FRET efficiencies by applying this method. Originally, this graph-theoretic algorithm has been used by its inventors for phenotyping white blood cells from pediatric patients from acute myeloid lymphoma (AML). As a result, they reached the conclusion that the intra-cellular signaling pathway markers are better candidates for characterizing the diseased states than the surface markers [16]. “Reduction of dimensionality” (RD) techniques for visualizing large data sets constitute another subclass of “artificial intelligence” (Figure 3). Historically the first RD technique, principle components analysis (PCA), originally published by Pearson in 1901, has already found wide-spread application in mass cytometry, spectral microscopy and spectral flow cytometry [17]. By applying “reduction of dimensionality,” Ni et al. also visualized different clustering of FRET negative and positive data points (cells). The significance of this visualizing approach is that there is no need for explicitly taking into account FRET efficiencies. Homogeneity of data can be inferred from merely the separability—or degree of confluence—of abstract geometric point sets to subsets. Data visualization has been accomplished by these authors with algorithms called t-SNE, Fit-SNE, UMAP, TriMAP, and PaCMAP [18]. Here, with the ratiometric FRET example, reduction of dimensionality means that while the input vector x → of the algorithm of Equation (1) has n = 3 dimensions, the output vector y → is of dimension m = 2. The aim of the RD algorithms in general is to replace the original high-dimensional (n) set of i = 1, … , N data-points ( x → i ) with another set of N data-points ( y → i ) with dimensionality m = 2 (or m = 3) while preserving the short- and long-range order, that is, the local and global structures of the original data points as “perfectly” as it is possible. To quantify the degree of preserving the original, high dimensional data structure, special functions—called cost-, loss-, penalty-, risk-, or decision-function—are introduced for comparing the information (or the “energy”) content of the x → , and y → data sets. Running the algorithm, the parameter set in the transformation Equation (1) is varied until the information or “energy” loss will be minimal. For example, for t-SNE the loss function is a special information difference, called “Kullbach-Liebler divergence” [18], comparing the information contents, obtainable from the probabilities of the k-neighborhoods in the high- and low-dimensional spaces. Interestingly the loss-functions of the abstract data-points can be decomposed into terms corresponding to short-, medium-, and long-range force gradients operating in real molecular clusters in the cell membrane, responsible for the attractive and repulsing forces with the corresponding energies from forces acting between the cluster elements [19]. Three VFP FRET pairs, CFP-YFP, YFP-RFP, and CFP-RFP expressed in TNFR1 as positive, high-FRET samples monitoring homo-associations of TNFR1 have been compared by these authors to cases where the donors (CFP, YFP) were expressed in TNFR1 and the acceptors (YFP, RFP) in CD27, as low-FRET, negative control samples. As their RD visualization shows, they obtained the degree of separations between the FRET positive and negative data points in the order of FRET efficiencies, that is, with the sharpest, medium, and the lowest separations corresponding to the CFP-RFP, CFP-YFP, and YFP-RFP FRET pairs, respectively [15]. Because the most widespread “artificial intelligence” technique, “supervised deep-learning” is carried out in “artificial neural networks” (ANNs), we give a more detailed account of these architectures [12]. ANNs are sequentially connected network of identical structural elements called neurons—non-linear (amplifying, noisy, and thresholding) elements—for realizing the vector–vector functional assignment expressed by Equation (1) (Figure 1, Panel A). Besides their sequential connectedness, another characteristic is that the neurons are organized into layers, the elements of which are, however, not connected. Each neuron in a layer receives signal from each element of the previous layer (transmitter neurons) amplified by a weight factor depending on the position of the transmitter neuron—or rather the relative distance of the receiving and transmitter neurons—and shifted by a constant, the “noise,” depending on the receiving neuron (Figure 1, Panel B). Mathematically this corresponds to a weighted averaging of the transmitter signals also symbolized by a scalar product of the transmitter signal vector and the weight vector. Finally, the receiving neurons of the given layer compare the detected average signal with a threshold, represented by an S-like or step-like function—called activation function—, and produce an output signal depending on the result of comparison, that is 0 or 1, depending on whether the result of comparison is sub- or supra-threshold (Figure 1, Panel B). A network architecture is generally comprised of an input layer, with as many neurons as the dimensionality of the input x → vector is, several receiving (medium) layers (called also hidden layers) with arbitrary number of neurons, and an output layer comprised of as many neurons as the output vector ( y → ) dimensionality should be. The purpose of this architecture generally is classifying the x → vector, into a class represented by an individual dimension of y → , specified by the maximal coordinate of y → . During their operation, ANNs in effect do reconstruction of the function in Equation (1), with an accuracy dictated by their “training” level. This function reconstruction might be guaranteed by the “universal approximation theorem (or law)” stating that any continuous function of several variables, say n, like the one in Equation (1), can be efficiently approximated by linear combinations of compositions of a fixed single variable function and a set of single valued n-dimensional linear functions with coefficients to be determined in the regression, or “training” process. This is the operation exactly done by the ANNs, with an additional provision that the fixed single variable function called also “activation function” should be strongly non-linear, like a sigmoid, S-like function or “step function” [20]. A common example for function approximation is the expansion in Taylor series, if the target function is differentiable “enough times.” The difference between the Taylor expansion and the general function approximation is that while in the former the approximation is valid at a point, in the latter, in an interval. “Convolutional neural networks” (CNNs) are essentially ANNs specified for image analysis (Figure 4) [21]. As to their architectures, they are comprised of several nested convolutions—that is, a stacked composition of a series of convolutions—completed with a conventional ANN. Recently several CNN-based fast (real-time) and robust FLIM analysis approaches have been developed [7-11]. With the conventional FLIM analysis methods like those based on, for example, nonlinear least-squares, maximum likelihood and Bayesian estimations, or phasors, analysis is done mainly off-side, after data registration. The ANN architecture for deep-learning has been borrowed from the behavior of the real biological neural networks found in humans and animals. It mimicks the learning procedure of their brain. Interestingly, cell populations of white blood cells in living organisms show similar network organization according to their operations inter-connected in hierarchical layers [16, 22]. Moreover, cell signaling receptors are also organized into hierarchical networks—interacting receptor clusters—on the surface of the individual cells. By analogy, modes of information transmission such as occurring via stochastic resonance (SR) in real neural networks, due to statistical synchronization, might be anticipated also in the millieu of cell surface receptor clusters [23]. Interestingly, the threshold level in the subthreshold SR phenomenon plays a role similar to that of the activation function in the ANNs [20]. By nature, FRET itself, applied for detecting receptor clusters, might also be described by ANNs. Historically, the first graph theoretical description of FRET has been carried out in the late 1970s by Gochanour, Andersen and Fayer (GAF model) [24]. Later, Bojarski and his co-workers developed further the graph theoretical description of FRET [25]. Because FRET might be a sequential process [26], and due to the proved suitability of FRET in information transmission [27, 28], the description of FRET in special boundary conditions by the ANN terminology might also be suggested and/or anticipated [29]. In the FRET field, ANNs might be fruitfully applied in the calibration of ratiometric FRET as well, whereby ANNs might be trained for the detection of the calibration factor α (or G) in situ on the FRET samples. Training here might be accomplished on the FRET samples themselves in the knowledge of the pertinent α factors. Financial support to László Bene, László Damjanovich for this work was provided by TÁMOP-4.2.2.A-11/1/KONV-2012-0045 project co-financed by the European Union and the European Social Fund, and OTKA Bridging Fund support OSTRAT/810/213, and science financing support 1G3DBLR0TUDF-247 by the University of Debrecen. The authors have no conflict of interest of any kind in the publication of this commentary.

Photons can convey information via their energy (or color), polarization, coherence, and timing. Energetics of molecules is dealt with spectroscopy, and the absorption and emission spectra act as fingerprints of molecules, which reflect changes in structure and environment with high sensitivity, being the spectra continuous in general. In conventional flow cytometry detection of fluorescence color has been mainly restricted to the detecting just a few discrete wavelength ranges (bands) often separated by gaps like "missing teeth." The enhanced information content meant by continuity of spectra has been first exploited in imaging when the output of a scanning microscope has been fed into a spectrograph and the whole emission spectrum has been recorded with a point detector at each pixel of the image [1, 2]. Recording emission spectra can also be parallelized by dispersing and projecting the light by a prism onto a pixel array of a CCD camera, onto an array of photomultipliers (PMTs), alternatively onto a multicathode PMT, through micro lenses [3, 4]. This latter method has also been applied in flow cytometry, where serially dispersive methods are not feasible due to the short dwell time of cells in the illuminating light beam. The finesse of the spectra on the wavelength scale is determined by the quality of the dispersive element and the number of detectors, or number of pixels in a CCD array. The fact that whole spectra are now recorded per cell in a flow cytometer, in dozens of channels instead of only a few, however, has drastically changed the attitude towards data analysis [5-7]. Classically fluorescence light is detected via just a few discrete channels from some fluorophores. However, due to the substantial width of emission spectra of the fluorophores, the contents of the different channels are not uniquely characterizing the individual fluorophores, but they are often characteristic mixtures of the individual emissions. Cleaning of signals of the different channels has been accomplished in hardware as well as software levels. At the hardware-, or "before acquisition" level, it covers the often not so easily done procedure, termed "compensation." At the software, or "after acquisition" level, it covers signal cleaning via extra calculations with the so called "spillage factors," applied, for example, in the ratiometric "Förster resonance energy transfer (FRET)" method, in the version "dual laser flow cytometric FRET" called FCET. Determination of compensation or spillage factors necessitates extra measurements on the pure spectral components. With a huge number of channels, as in spectral cytometry, however, such a correction is impossible. If the number of spectral components, fluorophores, is known in advance, with well-determined and time-constant spectra as their "fingerprints," and the components are not interacting, then the net spectrum is considered as a linear superposition of the component spectra (Figure 1) [5]. Alternatively, the net spectrum is considered as a vector, which can be expanded according to the component spectra as basis vectors, with the individual coefficients as the "coordinates," which are relative amounts, or concentrations in nature. Interaction between the components, for example, FRET, can be taken into account by appropriate extra relationships, "constraints" between the expansion coefficients. When the number of spectral components is large and unknown, another approach called principle components analysis (PCA) can be applied (Figure 2) [6, 7]. If a phenomenon is described by a few variables then they can be dependent on each other, the degree of which is quantified by the pair wise covariances. Their partial dependencies imply that their information content is overlapping, that is, information content of a variable can be influenced also by other variable. However, it is possible to find independent variables whose variances successively decrease. Independence here means that the directions in which the variables change the most are perpendicular to each other. Due to independence, information content can be directly assigned to the new variables in the form of their variances. Mathematically this procedure corresponds to finding the main directions of the covariance matrix called also "eigenvalue problem," or "main axis (canonical) transformation." In classical mechanics an analogous problem is finding the main directions of inertia of a rigid body via finding the eigenvalues of the inertia tensor. After establishing the order of the variables according to their information content, it is possible to reduce the data set, by leaving out those data having information below a given threshold. Utilizing the above principles, spectral flow cytometry became a routine approach of the today laboratory for solving "many variable problems" such as immune phenotyping [8, 9], detecting 3D gradients of cAMP [10], and analyzing solid tissue suspensions [11]. However, the application of spectral flow cytometry to FRET has remained a challenge. In their recent work, Henderson et al. [12] critically compare the detectibility of FRET in the same biological samples, with conventional and spectral flow cytometries. As to the biological nature of the investigated FRET samples, they belong to the "kinase assay by a FRET reporter" category. The structural building blocks of such an assay are depicted on Figure 3, Panel A. It is composed of a kinase target domain, which can be phosphorylated, a domain (sensor) recognizing the phosphorylated target, a hinge region connecting the target and sensor domains, and the donor (a cyan fluorescent protein, Cerulene3, briefly C3) and acceptor (a yellow fluorescent protein, cpVenus[E172], briefly cpV) fused to the ends of the sensor and target domains. Function is based on that the sensor domain binds the phosphorylated target, thereby reducing donor-acceptor distance, and enhancing FRET (Figure 3, Panel B). For monitoring AKT kinases, Lyn-AktAR2-EV is the "live" reporter, for probing the equilibria between the kinases and phosphatases (e.g., PTEN). Lyn-AktAR2-EV-D is the "dead" (or inactive) reporter possessing target moiety, which can not be phosphorylated, to determine baseline FRET. In these constructs, AktAR2 containing C3 and cpV as the FRET donor and acceptor, is the "core reporter" of AKT kinase activity in the cell cytoplasm. It has been extended with the Lyn and EV moieties for targeting the sensor from the cytosol into the cell membrane and spatially extending the dynamic range for FRET, respectively. For assaying PKA kinase activity the corresponding "live" (or active) sensor is LPAR-AKAR-WT, with LRRATLVD target domain, which can be phosphorylated, and FHA1 the recognizing, phosphate-sensing domain. The inactive assay here is LPAR-AKAR-mt, which contains a mutation in the target domain. According to the authors, these assays are applicable to monitor signaling pathways involving kinases (AKT, PKA) and phosphatases downstream to the B-cell receptor (BcR), and thereby for monitoring effects of drugs and gene knockouts, with an exceptionally good efficiency if combined with spectral flow cytometry. Basically the same principles of sensing have been utilized earlier for detecting cAMP levels via the H188 probe (Turquoise-Epac-Venus) [10]. Regarding the technique of flow cytometric spectral FRET, the authors find spectral FRET more versatile (or robust) and applicable than the conventional approach of ratiometric (or "3-cube") FRET. While conventional FRET can be computed only "offline," that is, after data collection, because of the need for spectral spillage factors and the calibrating G (or α) factor, spectral FRET determination can be carried out also in real time, for example, during data collection and cell sorting. The only prerequisite is the presence of a library of standard spectra ("end members") for the spectral unmixing. As to the analysis of spectral FRET data, the conventional approach is when the measured FRET spectra are decomposed into the linear combination of the spectra of the donor, acceptor and cell background, as "end members" (Figure 4, Panel A) [5, 13]. However, these authors noticed that FRET can be followed more sensitively, if the spectrum of the FRET sample is expanded according to the spectra of two special FRET samples—called "low" and "high" FRET spectra—differing in the FRET efficiency, but belonging to the same donor and acceptor fluorophores (Figure 4, Panel B). The dynamic range and sensitivity of the FRET measurement is determined by the difference in the two FRET efficiencies. Large difference favors for larger dynamic range and higher sensitivity. This approach has also the advantage that all factors mutually present in the "low" and "high" FRET samples and the interested "medium" FRET sample, drop out. This way spectral effects of cell background, and different markers for cell phenotyping—inasmuch as they are "spectrally inactive," non-interacting—can be eliminated. But for this, their spectra should be placed in advance in the library of spectra (of endmembers) used for spectral decomposition. Flow cytometry is a technique inherently applicable for multiplexing. Multiplexing in turn implies information transmission at a much higher rate, manifesting itself in an increased contrast between the subpopulations, called biochemical resolution [14-16]. Esposito et al. [15] gave a theoretical foundation of this notion by establishing a common framework for spatial and biochemical resolution based on Fisher information. According to this theory, degree of multiplexing can be quantitated. Increased multiplexing implies a finer degree of classification of fluorescence photons according to its properties, leading to an increase in Fisher information as well as to an increased degree in distinguishability in spatial and biochemical environments (Figure 5). Approaching the end of this short discussion, as a resume, we can say that significant step-forward already happened in the subject of spectral FRET in flow cytometry. Yet, there remained some open questions pertaining to the accurate theoretical treatment of spectral FRET, and ways of recovery, if it is feasible at all, of wavelength dependence of FRET. As to the mathematical analysis, the emerging utilization of phasor plots—introduced in the field of fluorescence lifetime—in spectral analysis and for describing fluorescence polarization might be expected to bring significant leap forward also in the field of spectral FRET [16, 18]. As to the photon properties amenable for information transmission, measurement of fluorescence polarization in flow cytometry has already been realized [19]. Time (pulsed) and frequency domain measurement of excited state (fluorescence) lifetime has also been recently demonstrated [20]. Unifying these facilities in a joint spectral platform would culminate in a hyper dimensional flow cytometry, as it has already been proven in microscopy [16]. Financial support to László Bene, László Damjanovich for this work was provided by TÁMOP-4.2.2.A-11/1/KONV-2012-0045 project co-financed by the European Union and the European Social Fund, and OTKA Bridging Fund support OSTRAT/810/213, and science financing support 1G3DBLR0TUDF-247 by the University of Debrecen. László Bene: Conceptualization (equal); methodology (equal); writing – original draft (equal); writing – review and editing (equal). Laszlo Damjanovich: Conceptualization (equal); investigation (equal); methodology (equal); supervision (equal); writing – original draft (equal); writing – review and editing (equal). The authors have no conflict of interest of any kind in the publication of this commentary. The peer review history for this article is available at https://publons.com/publon/10.1002/cyto.a.24561. The peer review history for this article is available at https://publons.com/publon/10.1002/cyto.a.24561.

Stochastic resonance in clusters of major histocompatibility molecules is extended by a more detailed description of adaptive thresholding and by applying the notion of suprathreshold stochastic resonance as a stochastically quantizing encoder of transmembrane signaling downstream of major histocompatibility molecules and T-cell receptors on the side of presenting and recognizing cells, respectively. The adaptive nature of thresholding is partly explained by a mirroring of the noncognate–cognate dichotomy shown by the T-cell receptor structure and the kinetic-segregation model of the onset of T-cell receptor triggering. Membrane clusters of major histocompatibility molecules and T-cell receptors on their host cells are envisioned as places of the temporal encoding of downstream signals via the suprathreshold stochastic resonance process. The ways of optimization of molecular prostheses, such as chimeric antigen receptors against cancer in transmembrane signaling, are suggested in the framework of suprathreshold stochastic resonance. The analogy between Förster resonance energy transfer and suprathreshold stochastic resonance for information transfer is also discussed. The overlap integral for energy transfer parallels the mutual information transferred by suprathreshold stochastic resonance.

A new method of flow cytometric dual-laser FRET calibration is presented based on an information theoretical description of the FRET signals. This method belongs to the so called two-channel or ratiometric FRET methods, whose crucial and common element is the determination of a calibration factor called α (alpha- or G-factor), to place the detected FRET signal on the absolute scale of efficiency. Generally α is determined by extra cell samples labeled with only donor and only acceptor, where the donor-acceptor ratio is known. Alternatively, when the donor-acceptor ratio is not known, standard donor-acceptor FRET pairs of known FRET efficiency can also be used for determining α. In our approach, there is no need for extra information presented by the known acceptor-to-donor ratio or the standard FRET efficiency. Our approach proceeds solely on the signals of the interested FRET-pair applying only a single FRET sample, not necessitating extra ones. The missing information of extra cell samples is replaced by an information theoretic balance equation written for the actual FRET sample. Our method has been proven to be robust, inasmuch as both donor and acceptor appear in adequate levels in the FRET sample used for finding α.

Enhancements of hetero-fluorescence resonance energy transfer (FRET) and homo-FRET have been observed upon excitation with circularly polarized light as compared to excitation with the linearly polarized one in the context of fluorescent dye-labeled cell surface receptors. The enhancement effect has been gradually evolved with changing ellipticity of the exciting light from zero of the linearly polarized light to unity of the circularly polarized one. The measurements have been carried out in a single-laser dual-anisotropy scheme in a flow cytometer, where polarized intensity components in the donor and acceptor channels have been measured simultaneously. For hetero-FRET, the FRET-enhancement effect revealed by a combined detection of donor quenching and sensitized emission of the acceptor has been corroborated by a parallel increase in donor anisotropy and a decrease in acceptor anisotropy. As to homo-FRET, the FRET enhancement, inferred from increased depolarizations of anisotropies measured in two different emission bands, centered at a shorter and a longer wavelength, has also been corroborated by a parallel reduction in "the longer to shorter wavelength" anisotropy ratio. The observed enhancement effects are explained by a relief of orientation mismatch between the FRET donors and acceptors, a phenomenon observable when excitation is depolarized as compared to the linearly polarized one, and a concomitant "homo-FRET-amplified hetero-FRET" phenomenon, both based on an increase in the orientation factor (kappa(2)) for FRET. Circularly polarized light represents a depolarized mode of excitation leading to a photo-selected orientational distribution of the donors matching better with that of the potential acceptors. The magnitude of this effect is dictated by the anisotropy of the orientational distributions of the donor and the acceptor. By comparing FRET with excitations of different helicities, a new steady-state method for the detection of molecular dynamics is presented. The method can equally be used in flow cytometers and fluorescence microscopes equipped with excitation with helical light even when the detection is not polarized. The conventional formalism of anisotropy detection in the T-format at vertically polarized excitation has been extended to linearly polarized excitation at different polarization angles and depolarized excitations.

A quick and robust approach for the simultaneous detection of donor and acceptor anisotropies and FRET efficiency is presented based on changing the angle of polarization of the exciting light in a single-laser dual channel ratiometric detection scheme of FRET in a flow cytometer. The convenience of the method lies in that for the extra assessment of anisotropies it does not necessitates alteration of the detection side of the optics conventionally used in measuring FRET in the steady state. The detection of anisotropies is pushed to the side of excitation where anisotropies are enabled by just a few sequential measurements at different polarization angles of the exciting light. The power of the method is illustrated by comparing results on the homo-associations and inter-subunit FRET on the MHCI receptor on the surface of Kit-225K6 T cells obtained with the angle-resolved approach to those obtained by the dual-T format approach as a validation. In flow conditions, but not in imaging microscopy, a minor drawback of this method is that due to the sequential nature of anisotropy detection, the mutual cell-by-cell correlations of anisotropies with each other and with FRET are lost. The merit of the approach is that besides the degree of molecular associations probed by the FRET efficiency, information can also be gained on the rotational dynamics and extent of homo-FRET prevailing in the the donor and acceptor dye systems during the hetero-FRET process, and as a consequence, orientation factor for FRET can also be estimated. FRET efficiencies at the different polarization angles are shifted depending on the donor and acceptor anisotropy, enabling quantitation of anisotropy changes by FRET efficiency. Attention is called for polarization biases when using even depolarized excitation and detecting not concerning with fluorescence polarization. When established in polarization contrast microscopy, the approach might be applied for also controlling FRET. A new formula for the determination of the sensitivity calibration factor for FRET α (or Get) has also been deduced based on the donor and acceptor anisotropies.

László Bene1,2* and László Damjanovich1 Author Affiliations 1Department of Surgery, Faculty of Medicine, University of Debrecen, Debrecen, Hungary 2Department of Biophysics and Cell Biology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary Received: November 18, 2020| Published: November 25, 2020 Corresponding author: László Bene, Department of Biophysics and Cell Biology, University of Debrecen, Debrecen, Hungary DOI: 10.26717/BJSTR.2020.32.005213

About the common features behind the mechanism of molecular rotors, photoswitching of engineered fluorescent proteins (GFPs), and Förster resonance energy transfer (FRET). Besides explining the common mechanism, we also offer a new method for increasing sensitivity of viscosity determination even in living cells, by the combination of polarization energy transfer (polFRET) method and a molecular rotor dye either as an energy donor or acceptor.

Fluorescence lifetime is an important contrast modality of selectively detecting different types of dyes and their interactions, where possible contaminating effects of hardly controllable factors such as exciting light flux and local exciting dye concentration are absent (1, 2). Time- and frequency-domain detections of fluorescence lifetime have been elaborated both in microscopy and flow cytometry (2-5). Phasor plot is a graphical replacement of the fluorescence decay curve of a fluorescent system. Although excellent accounts of phasor plots are existing in the literature (6, 7), we recast it now from the viewpoint of the general systems and communication theory. The approach of systems theory is that the examined object is treated as a black box, and the structure of the black box is inferred from the distortion of shapes of signals introduced into the black box (8) (Fig. 1). The shape of the input signal is distorted upon interactions with the elements of black box. The types and strengths of interactions can be found via a careful analysis of the shape distortions of the output signal in a noninvasive manner, not necessitating structural changes of the black box. The black box can also be conceived as an information channel influencing the transmitted information meant by the shape of input signal and the received information represented by the shape of the output signal. For the sake of concreteness, let us first mention an LR-circuit (9) (first row of Fig. 1). Upon excitation of the circuit with a square pulse, the elicited current will show a degree of smoothing of both the front and rear of the input signal, dictated by the relaxation time constant, τ. The relaxation time expresses the degree of inertia of the system against the perturbation and here is dictated by the inductivity to resistance ratio (L/R) (9). As a second example, let us take a microscope objective (second row of Fig. 1). The image of a rectangular brightness distribution of an object placed in the focal plane will no more be rectangular in the image plane, but more-or-less blurred at the edges. The degree of blurring is characterized by the critical distance (d)—or reciprocal resolving power—of microscope resolution, which is dictated by the ratio of the detected wavelength and the objective's numerical aperture (10, 11). As the third example, let us take a fluorescent dye solution in a cuvette, excited by a square light pulse at a suitable wavelength for eliciting fluorescence (third row of Fig. 1). Then, the shape of the evoked fluorescence signal will also show distortions characteristic of the dye solution. At the front of the signal, there is no distortion because of the instantaneous absorption of photons (10−15 s). However, at the rear, some lengthening of emission is seen governed by the storage time of excitation, the fluorescence lifetime, τ, which in turn is defined as the reciprocal of the sum of radiative and nonradiative rate constants, kf and knr, respectively. A key to understanding of phasor-plots is the observation that the output signal of a black box can be forecasted for any input signal shape if the systems response to an infinitely narrow excitation pulse (Dirac- or δ-pulse) is known (Fig. 2A). This function is called impulse response function or weight function h(t), and considered as a fingerprint of the system (8-11). Its significance lies in that, in the knowledge of it, the response of the system mathematically can be found out for any input signal shape via the operation called convolution. During convolution, each particular g(t0) value of a g(t) function is replaced by a weighted average of the whole g(t) function with a weighting function h(t) centered on the particular t0 time point. This operation is analogous to smoothing clothes with an iron: where g(t) is the cloth with the creases to be removed, and the weight function h(t) is the iron. An important mathematical theorem is that of convolutions. It states that any convolution can be transformed into the product of two complex numbers, the so-called Fourier-transforms of the convolved quantities, with the consequence that any time function of the black box can be rendered visible by appropriate geometric features in the two-dimensional plane (8-11). A commonplace example for Fourier-transform is splitting up into different color beamlet components of a white light beam by a prism, or a drop of water. We saw above that the impulse response or weight function represents the system's structure as a finger print. Its Fourier-transform is called the transfer function. Because this is a complex number, it can be written as a product of a modulation m and complex exponential term containing a phase ϕ (Fig. 2B). The traditional way of representing lifetime measurement data is separately representing the modulation and phase in a common frame as monotonously decreasing and increasing functions of the circular frequency (12). However, by expanding the complex exponential of the phase via Euler's rule into the sum of a cosine (real) and a sine (imaginary) term, and by multiplying them with the modulation term, the transfer function can be resolved into the sum of a real and an imaginary term, called B and A, respectively (Fig. 2C). This second alternative representation of the transfer function is called a phasor-plot (or AB-, SG-, ND-plot) (6, 13). In the case of image formation in a microscope, the δ-pulse corresponds to a point in the object plane. The impulse response of the microscope is the point-spread function (PSF) whose width is proportional to the critical distance given by the Abbe's formula. The H(ω) transfer function for the microscope is the Fourier-transform of the PSF, called now optical transfer function (OTF). Imaging quality of microscopes can be improved by purposeful alteration of the OTF, called spatial filtering (9-11). We introduced phasor plots above as a graphical representation of the transfer function of the system, which in turn has been obtained by Fourier-transformation of the system's impulse response function. However, it can be obtained without any assumption on the functional form of the impulse response by a harmonic excitation of the system, that is, carrying out the Fourier-transform at the hardware level, in a phase-modulation measurement (Fig. 3A). Here, both the demodulation and phase shift can be determined from either the fluorescence response curve or the associated demodulation-phase curve pair (Fig. 3B) and AB-plot (Fig. 3C) at the circular frequency of excitation (ω0), from which the apparent phase and demodulation lifetimes can also be determined. In contrast, the single δ-pulse excitation above only fixed the shapes of these curves and did not fix the actual values of phase, demodulation, and associated lifetimes. However, this can be made with a trick. If the single δ-pulse is repeated many times, resulting in a “δ-comb,” then the pulse series acts similarly to a harmonic excitation, with a circular frequency dictated by the pulse repetition rate. At this circular frequency, the phase and modulation lifetimes can be read off analogously to the harmonic case from the phase-demodulation curve pair or from the AB-plot (14). We saw above that the A and B quantities are quadrature components of the complex transfer function, which is the Fourier-transform of the impulse response or weight function of the dye solution. If A is plotted against B, then the complex plain can be divided into three regions (Fig. 4A). For a single component solution having a single fluorescence lifetime there is a strict relationship between the demodulation and the phase: m = cos(ϕ). Consequently, the corresponding (m, ϕ) pairs constitute a circle, the “universal circle” of radius 0.5, and origin of (0.5, 0), on which fluorescence lifetime increases by proceeding with ϕ anti-clockwise from horizontal direction (ϕ = 0). The m = cos(ϕ) relationship for the “universal circle” conveniently understandable, for example, because the horizontal diameter of the circle is seen at 90° from all points of the circle, according to Thales' theorem. Points inside the “universal circle” obey the m < cos(ϕ) relationship, referring to ground-state heterogeneity or the presence of Förster resonance energy transfer (FRET) for the donor (measured at the donor side). In these cases, the impulse response function of the system is composed only of positive amplitude components. However for excited state reactions such as solvent relaxation and FRET toward an acceptor (measured at the acceptor side), phasor points can also get outside of the circle, obeying the m > cos(ϕ) relationship (6, 7, 15). In the case of excited state reactions, the impulse response function contains also negative amplitude (pre-exponential factor) component(s), representing indirect excitation by the molecular environment. Physical rotation can also be conceived as a special energy transfer process between the different orientations of the oscillating molecular dipole. The parallel polarized component of fluorescence decays via both the natural decay of the excited state, and via the molecule rotating out from the orientation of parallel emission. The corresponding phasor point falls inside the circle mimicking ground state heterogeneity. In contrast, the perpendicularly polarized component of fluorescence decays via the natural decay of the excited state, and via the molecule rotating into the orientation of perpendicular emission, the latter described by a negative amplitude, rendering the corresponding phasor point to fall outside of the circle, like for FRET toward the acceptor (16). Ground state heterogeneity and FRET from the donor can be distinguished via the geometrical shapes defined by the phasor points. For ground state heterogeneity, they constitute straight line intervals with the cutting points of their elongations with the circle giving the lifetimes of the mixed components (12, 13) (Fig. 4B). For FRET from the donor, phasor points constitute banana-like curved geometrical shapes (18) (Fig. 4C). For an explanation of the latter, we should think of that, in the absence of FRET the phasor point is the mixture of pure donor and pure background phasors locating on the circle to left and to the right, dividing the connecting bisector according to the lever rule: the distance of the mixture point from one end point of the bisector is proportional to the fluorescence intensity for the opposite point. Because of this, the starting point is located to the left inside the circle, but close to the perimeter. The endpoint of the FRET trajectory is the mixture of the close to 100%-quenched donor and background. The phasor point representing this mixture locates to the right, inside the circle, close to the perimeter. Besides, the starting and the end points are located such a way that their connecting intersection cuts the circle at the pure donor and background points. At intermediate FRET efficiencies the phasor is a mixture of the quenched donor and background points. In their work, Nichani et al. (in this issue, page 1265) developed further the concept of FRET trajectory by sensitizing FRET for indicating the time evolution of a biological process called apoptosis. The development of apoptosis is indicated by the level of caspase-3 enzyme, which in turn is indicated by a FRET probe via the degree of FRET relief achieved by scissoring by caspase-3 the linker domain fusing together the donor and acceptor, the three forming an apoptosis-indicating FRET bioprobe. In the bioprobe, engineered green fluorescent protein serves as FRET donor and Alexa Fluor-546 as the acceptor. For truly indicating caspase-3 levels, prerequisites are the high enough dynamic range ensured by the large starting FRET efficiency, the low enough bioprobe level for avoiding cross-FRET contamination between the nearby intact probes as well as between the intact probes and the liberated acceptors and donors. There are also technical requirements such as the spectral purity of the donor channel. As they demonstrate, phasor plots can be advantageously exploited also in flow conditions at a single excitation frequency for real time tracking a signaling event. However, the true interpretation of the phasor plots requires also the precise knowledge of all components of the donor fluorescence. The multiplexing capability of flow cytometry is well illustrated by the authors via correlating donor fluorescence lifetime with FRET-channel fluorescence, as an indicator for the presence of acceptor in the bioprobes. In steady state flow cytometry and fluorescence microscopy, FRET efficiency is determined generally in a simple donor quenching experiment or in the ratiometric FRET scheme involving two or three signal channels. In the latter case, however, absolute FRET efficiency can only be determined in the knowledge of a calibrating factor called α (or G), responsible for balancing quantum efficiencies and collection efficiencies of fluorescence for the donor and acceptor (19). Direct measurement of FRET efficiency via fluorescence lifetime obviates the need for α. Alternatively, fluorescence lifetime might also aid in determining α, and consequently, instrumental spectroscopic parameters such as fluorescence transmission efficiencies, or absorption coefficient of the donor and acceptor prevailing in the cellular milieu. The α-factor is also an important parameter for determining the donor-acceptor molar ratio of the actual FRET sample in the ratiometric FRET scheme. Besides the role in FRET measurements, fluorescence lifetime has also an important role in converting fluorescence anisotropy values to rotational mobilities. In fluorescence spectroscopy, phasor plots have first been introduced by D. Jameson and his colleagues, but before that, they were also applied in relaxation kinetics, chemical and dielectric, under the name of “Cole-and-Cole plots” (6, 7). Recently these plots have been revitalized by the fact that their usage greatly widens the applicability of single-frequency fluorescence lifetime imaging microscopy (FLIM) and the realization that phasor plots can be applied not only in the frequency domain FLIM, but also in time domain FLIM (14, 18). Theoretically, patch-clamping in electrophysiology might also be a field for a fruitful exploitation of the phasors. Based on the close correspondence between open ionic channels and excited dyes, the decay kinetics of open channels is described by the same formalism as those for fluorescing dyes, by taking over the role of fluorescence lifetime by the mean open time of channels. In addition to the model-independent, that is, free of assumed functional form, characterization of channel kinetics, for example, collective behavior of channels (cooperativity), synchronization of channel openings—the counterparts of excited state dye interactions—as the function of their cluster size might be revealed by the graphical counterparts of the decay curves. Besides, the direct application of the phase-modulation detection of currents, as an analogue of phase-modulation FLIM, might also convey some extra information. Homo-FRET is a FRET process taking place between dyes of identical type having small Stokes' shift. In the limiting case of high excitation intensities close to saturation, homo-FRET might be exchanged for interactions between excited dyes in close proximity, called super/sub-radiance or super/sub-fluorescence. In this case, radiative rate might be either increased or decreased due to emission dipole synchronization by the net effect of the dye local fields, the exciting light, the emitted fluorescence, and the morphology of the dye cluster (20). Even if the mean excited state lifetime of the dyes stays constant, the lifetime heterogeneity might increase manifesting in a broadening of lifetime distributions. Phasor plots might represent these events by an analogue broadening of distributions and falling points outside of the universal circle. Taking together, flow cytometry made a leap-forward with the introduction of spectacular representation of FRET-processes in the complex plane of phasor plots. Financial support to László Bene for this work was provided by TÁMOP-4.2.2.A-11/1/KONV-2012-0045 project co-financed by the European Union and the European Social Fund, OTKA Bridging Fund support OSTRAT/810/213, and science financing support 1G3DBLR0TUDF-247 by the University of Debrecen. We are thanking for Prof. J. Szöllősi for the careful reading our manuscript. László Bene: Conceptualization. Laszlo Damjanovich: Conceptualization.

Highly conserved 2D receptor clusters (membrane rafts) of immunological signaling molecules with MHCI and MHCII antigens as their cores have been observed in the past on the surface of T- and B-cell lines of lymphoid origin, as well as on cells from patients with colon tumor and Crohn's disease. Conservativity is related to the ever presence of MHCI molecules. Although they are suspected to play a role in maintaining these clusters and facilitating transmembrane signaling, their exact role has been left largely enigmatic. Here we are suggesting stochastic resonance (SR), or "noise-assisted signal detection", as a general organizing principle for transmembrane signaling events evoked by processes like immune recognition and cytokine binding taking place in these clusters. In the conceptual framework of SR, in immune recognition as a prototype of transmembrane signaling, the sea of self-peptide-MHC complexes around a nonself-peptide presenting MHC is conceived as a source of quickly fluctuating unspecific signal ("athermal noise") serving the extra energy for amplifying the weak sub-threshold specific signal of the nonself-peptide presenting MHC. This same noise is also utilized for a readjustment of the threshold - and also the sensitivity and specificity - of detection by a closed loop feedback control of the TcR-CD8 (CD4) proximity on the detecting T-cell. The weak sub threshold specific signal of nonself-peptide presenting MHC is amplified by the superposing unspecific signals of the neighboring self peptide-MHC complexes towards the T-cell receptor as the detector. Because in a successful detection event both self- and nonself-peptides are detected simultaneously, the principle of coincidence (or lock-in) detection is also realized. The ever presence of MHC islands gets a natural explanation as a source of extra power - in a form of "athermal noise" - needed for coincidence detection and frequency encoding the evoked downstream signals. The effect is quite general, because the actual type of molecules surrounding a chief signaling molecule - like nonself-peptide holding MHC, interleukin-2 and -15 cytokine receptors (IL-2R/15R) - as the fluctuating interaction energy sources is immaterial. The model applies also for other types of signaling, such as those evoked by cytokine binding. The phenomenon of SR can also be interpreted as sampling of a low frequency, specific signal with a high frequency unspecific signal, the "noise". Recipes for identifying other forms of SR in membrane clusters with biophysical tools are recommended.

EVERY molecule, cell, and cell organelles are subject to some level of mechanical pressures and forces. As a relatively new branch of science, biomechanics, is dealing with measurements of forces at different levels of organization of the living state and studying transmission of force through the cell membrane toward the cell interior (mechano-transduction), as well as the conversion of mechanical signals to electric and chemical ones, that is, signal transductions evoked by mechanical forces (1–3). The action of stretch activated ion channels can serve as a classical example for a mechanical–electrical signal transduction. In order to monitor these types of signaling, an important step forward is the development of biosensors capable for mechanical force measurement at the molecular level, even inside the living cell. An important class of force sensors is based on Förster resonance energy transfer (FRET) (1–3). Recent applications of FRET for mapping interleukin2-interleukin-9 receptor (IL-2R-IL-9R) complexes, for revealing spatial gradients of cyclic adenosine monophosphate (cAMP) second messenger complexes, and for imaging flow cytometry by light-sheet microscopy are exemplified in Refs. (4–6). A possible application of FRET as a photoswitching agent of genetically engineered fluorescent proteins (VFPs) is described in Ref. (7). The basic characteristics of these methodologies is that a tension sensitive FRET-ruler—a tension sensor—is positioned via genetic engineering in the target molecule in which the tension is intended to be measured. The intracellular tension sensor has a flexible natural or artificial linker region, connecting the donor and acceptor—genetically engineered visible fluorescent proteins (GFPs)—at its two ends, which as a whole is expressed in the target structures in the living cell (Fig. 1). The main assumption is that the stress on the target molecule should change the length of the linkage, as a spring, in such a degree that can cause a measurable change in FRET. The main parameters of a sensor— the lower and upper limits of detectable forces, that is, the dynamic range and the magnitude of FRET response to unit stress, that is, the sensitivity—are determined by the stiffness (spring constant) and length of the linker, as well as the FRET efficiency, quantified by the characteristic Förster-distance R0. As a general rule, while increasing the characteristic Förster-distance R0, FRET efficiency is increased, increasing the length and stiffness (“spring constant”) of the linker protein, FRET efficiency is reduced. A specific example for high tuning a tension sensor is shown by the group of Hoffman et al. (8,9). They developed and further improved a vinculin-based tension sensor (VinTSMod) to measure force transmission of vinculin, which bridges adhesion receptors in the cell membrane and the actin filaments of cytoskeleton. Here, the tension sensor module itself is TSMod— originally developed by Grasshoff and co-workers (1)—in which the elastic spider silk protein flagelliform (GPGGA8) is used as the flexible linker domain, the spring, with mTFP1 (blue) and Venus (yellow) fluorescent proteins attached to its ends as the donor and acceptor. The “Vin” refers to flanking the ends of TSMod before and after the GFPs with the head and tail of vinculin (Vh, Vt) as the attaching sites. Binding Vh to the intracellular domains of adhesion receptors, and Vt to actin filaments of the cytoskeleton, by expressing this sensor in vinculin −/− MEF

Orientation factor (κ2) for FRET from a rotating donor dipole, transferred helicity of the donor field and torque exerted on the acceptor by the donor have been investigated in the framework of classical electrodynamics. It is shown that for rotating dipole, κ2 is significantly higher as compared to linear dipole independently of the orientation distribution of the donor and acceptor and whether the static or the dynamic rotational regimes are used for averaging κ2. By this property of κ2, FRET serves as an example for a phenomenon where local field interference may take place in a "natural" way for emitters possessing rotating dipoles in their excited states by nature. The overlapping spatial distributions for the helicity of donor local field, torque exerted on the acceptor by the donor and for the FRET orientational factor suggest that transfer of both energy and helicity take place predominantly in the plane of rotation by keeping the original direction of helicity, i.e. in accordance with the conservation law for helicity. Orienting FRET has been proposed by engineering local field structure by using elliptically polarized light for donor excitation or by using linearly polarized light coupled with electromagnetic modification of the donor environment. The phenomenon of increased κ2 can be exploited for checking helicity conservation for different FRET donors without the need for polarized detection optics. Modulation of FRET with changing ellipticity of the excited donor state might supply structural and dynamical information on the orientational distribution of dye-holding matrices even on the surface of living cells, e.g. on the level of cell surface receptor clusters. Furthermore, it might also be exploited in sensing local electromagnetic fields. Rotating excited donor states might also facilitate turning on photoswitchable acceptors.

Molecular biology has been revolutionized by the discovery of a new family of fluorophores termed fluorescent proteins (FPs). The value of this kind of fluorophores rests in the possibility to genetically attach it to virtually all kinds of proteins and detect it relatively easily via fluorescence spectroscopy not interfering with life processes 1, 2. Besides the more conventional, simple type of FPs with fixed absorption and emission characteristics—that is, with constant absorption and emission wavelength ranges, and constant absorption coefficient and quantum efficiency—there are also those whose photophysical properties can be modulated by light. This FP subfamily is called molecular highlighters. This subfamily can even be further classified according to whether the given photophysical constant is permanently or reversibly modified, or whether the modification of a photophysical constant is followed by a spectral change or not, giving rise to the “photoactivatable,” “photoswitchable,” and “photoconvertible” classifications 3. The invaluable property of highlighters is that their photophysical changes can be used for specifically tagging them when monitoring different molecular biological processes: for example, substrate transfer from one compartment to another one in single particle tracking and FRAP experiments 4. Or in FRET experiments when the specific tagging means a controllable appearance and disappearance of a FRET acceptor—in a measuring scheme called acceptor photobleaching FRET (apbFRET)—making possible molecular level paired comparison of FRET experiments 5. The specific tagging attribute is utilized also in super-resolution imaging modalities called “photoactivation localization microscopy” (PALM) and “stochastic optical read-out microscopy” (STORM) 6-10. In PALM (Fig. 1), FPs of a cluster are activated stochastically such that the surface density of simultaneously activated emitters is low enough to ensure that there is no overlap between their point spread functions (PSF), that is, light is detected from spatially well separated single molecules. After sequentially registering the images of a large number of single molecules, the location of each one is determined by averages, and the image of the cluster is reconstructed by plotting these averages in a single frame, in a process analogous to “pointillism” in painting. Resolution is enhanced at the price of a priori knowing that only images of spatially distinct—that is, at separations larger than PSF width—single molecules are recorded in each time frame. Besides the inevitable advance in spatial resolution enhancement, a drawback of the method is that it is extremely time consuming, requiring hours of measurement time in the initial demonstrations. The need for optimizing the spectroscopic conditions for the simultaneous fulfillment of several requirements such as more efficient photoactivation for a more precise spatial tracking of the molecular ensemble, high enough number of collected photons ensuring the good signal-to-noise ratio, and the shortest possible imaging time, is inevitable in these types of applications. Single molecule localization principle. Panel A: Overlapping intensity distributions,—point-spread functions (PSFs)—detected from two dye molecules at a close proximity (green, yellow dashed). The overlap of the two curves indicates that the separation is smaller than the critical distance for resolution. When simultaneously detecting the two dyes in the same spectral range the sum of the two curves is observed (red), and the two dyes cannot be discerned. According to the Abbe criterion, the PSF width is ca. half of the detecting wavelength (λ/2). Panel B: However, if the color of detection or the time of detection is different for the 2 dyes—“color or time-tagging “—than the Abbe criterion can be circumvented and the two dyes can be resolved even at distances smaller than the Abbe limit. In other words, by knowing in advance that the green and yellow distributions (PSFs) belong to two dyes, their locations can be determined as the centers of their corresponding PSFs (black downward arrows). The error of these means—the width of the two narrow red curves—is dictated mainly by the respective photon numbers (N, the area under the green and yellow curves) according to law (7). This calls for the critical role of the detected photon-number in these approaches. The red curves can be deduced from the “parent” green and yellow ones by increasing the amplitude and reducing the width c.a. -fold. In PALM, dyes are switched on successively, sparsely enough to have only a single emitting dye within a PSF each time. The advantage and also complexity of light emission of FPs originate from their special structure (Fig. 2). Their common theme is that of a fluorophore composed of two rings coupled together alongside an α-helix and enclosed in a β-barrel. As compared to the conventional fluorophores having spectral properties not modifiable with light, they have two main distinctive attributes: 1) While in a conventional dye, the chromophore rings forming a stiff sheet are not capable of relative rotations, in an FP they are able to rotate. 2) For a conventional dye dissolved in water, solvent-solute interactions—dipole polarization and hydrogen bonding with water—are relatively weak, and by-and-large are the same in ground and excited states. In contrast, for the chromophores of FPs, they are strong—the above interactions with close-by amino acids of the α-helix and β-barrel in addition to water—and different for the ground and excited states. In chemical kinetical terms, while conventional dyes exist mainly in a single rotational state, chromophores of an FP can be found in a series of rotational isomeric states represented by different spectral properties and interconnected with transitions evoked by light illumination 3, 11. These kinds of interactions can also be found with the conventional dyes, but in much weaker forms, collected in the terms “red-edge effects” or “solvent effects” on which “site-selection spectroscopy” rests 12. Spectral properties of FPs can be tuned by engineering the type of amino-acids surrounding the chromophores and dictating the palette of solute-solvent interactions: their state of protonation, hydrogen-bonding, extent of double bonds, and the number of available rotational isomeric states. Schematic illustration of the structural difference between a conventional organic dye and a photamodulatable fluorescent protein fluorophore. Panel A: The structural formula for a conventional organic dye, such as fluorescein, rhodamine. The core structure (xanthene) responsible for light emission is a rigid planar sheet. In free solution conditions, only global rotations can exist, with a constant molecular neighborhood and the same solvent interactions at all global torsion angles τ1. The rings (xanthene) holding the extended π-conjugations are shaded with green. The fourth phenol ring in perpendicular position (white) does not take part in emission. Panel B: In contrast, in a typical fluorescent protein, the 2 chromophore rings—benzene and one imidazol—are substantially loosely connected, making possible for them to rotate around each other. A series a conformational (rotational isomers) and protonated states might exist which are stabilized by different hydrogen bondings toward the amino acid wall of the surrounding β-barrel (grey cylinders). Torsional rotations around the horizontal rotation axis, labeled τ1, switch the chromophore from the “cis” to the “trans” conformation. Altering the extent of π-conjugation, protonation state and interactions with the environment (solute–solvent interactions, quenching) these changes manifest themselves also in differences in spectroscopic properties such as extinction coefficient, quantum-efficiency, fluorescence lifetime, color of absorption and emission, and also blinking. Such rotations can be evoked indirectly, by the increased torque exerted by the environmental residues on the increased excited state dipole. Alternatively, torque might be exerted directly, by the exciting agent, such as circularly polarized light, local field of a FRET donor, or the evanescent wave in TIRF method, types of excitations capable also of transferring angular momentum in addition to energy. Panel C: Level scheme for the fluorescence of the conventional dye of Panel A. Here, there is only a single rotational angle (τ1 = 0°). The vibrational structure of the electronic excited states are omitted. Blue (green) arrow: absorption (emission). Panel D: Level scheme—potential energy versus torsion angle curves (τ1 = 0°)—for a fluorescence protein chromophore depicted in Panel B. The rotational states lead to opposite undulations in the energy levels of the ground and excited states, S0 and S1, respectively. The scheme is actually a simplified version of the asFP595 reversibly photoactivatable fluorescent protein [11]. This protein fluoresces in red upon green excitation for a while in the “cis” state, then by going over to the “trans” state, it switches off. It can be switched on with blue light in the “trans” state, but this absorption event is not followed by fluorescence. The working cycle—“molecular motor”—can be explained as follows: Upon excitation with green light in the “cis” state, the chromophore either fluoresces in red, or suffers non-radiative de-excitation into the “trans” state at a τ1 = 90° torsion angle, indicated by the orange arrow. At τ1 = 90° the potential energy curve of the excited state has a specific feature: it touches that of the ground state as a junction, making non-radiative relaxation via internal conversion possible. Since in the “trans” state the chromophore cannot be excited with the green light, after a while all chromophores will accumulate in the dark “trans” state. In the switching-on phase in the “trans” state, upon excitation with blue light, the chromophore is only capable of non-radiative relaxation into the “cis” state through the junction at τ1 = 90°. Although this scheme has been devised for asFP595, the authors state that it might be considered general [11]. In a previous work, Renz et al. 8 developed a binary-photoactivatable PA-GFP + PA-Cherry fusion construct as an internal control for single molecule counting with PALM. Their idea is that, if they tune the experimental conditions such that the counts of PA-GFP fluorescence linearly changes with those of PA-Cherry, then the green-to-red ratio of single molecule counts can be determined for an arbitrary system, one member of which is labeled by PA-GFP and the other by PA-Cherry via normalizing the green-to-red ratio of the arbitrary system to that of the control. By applying this approach in PALM, single molecular level stoichiometry of homo- and hetero-clusters can be revealed. A similar idea has been used in the field of fluorescence resonance energy transfer (FRET), when FRET efficiency is normalized to that of a one-to-one donor-acceptor system such as the MHC I light and heavy chains on the cell surface or an EGFP-mRFP1 or ECFP-EYFP fusion protein 13 to calibrate the sensitivity factor α for FRET. In single molecule microscopy, the determination of the absolute number of proteins in cells or in a protein cluster is an important question. However, several factors hinder counting the absolute numbers of proteins. Imperfect maturation or incomplete photoactivation of the FP markers, or residence of the FPs in long-lasting dark states leads to underestimated protein counts. Vámosi et al. 14 elaborated a method to determine the fraction of EGFP molecules residing in long-lasting dark states by using fluorescence brightness analysis of EGFP oligomers. On the other hand, if a photoactivated fluorophore returns to a fluorescent state from a long-lasting dark state, and is counted repeatedly, it can cause overestimation of protein numbers. Baumgart et al. 15 varied the label density in STORM to distinguish real protein clusters from artefactual clusters appearing due to repeatedly counting blinking fluorophores. Their third result is related to establishing the proper experimental conditions for photoactivation. They showed that photoactivation efficiency depends not only on the total photon dose of illumination but also on whether the dose is fractionated in time or in space. They observed more efficient photoactivation with repetitive excitations (“interleaved or pulsed activations”) in a confocal microscope as compared to continuous intense excitation within a short period of time with the same amount of photons. Analogously, photoactivation proved to be more effective with illumination via a wide field illuminating system exciting molecules stochastically over a longer period of time, as an example for the spatial fractionation. These results are in good accordance with the recorded dose–response curves of activation where the efficiency of photoactivation reaches a maximum—the place of “resonance”—at a given photon dose (Fig. 3). The existence of the maximum can be explained by an intensity dependence of the rate constant for the “on” state of the fluorophore as well as for the rate constant for photobleaching. That the rate constants for both the “on” state and photo-bleaching are higher at greater photon doses is in accordance with a serial triggering model of these processes which in turn imply the validity of the rotational isomer state model of the fluorescent protein. That photobleaching might have to do with the above maximum point is corroborated by the observation that photoactivation efficiency is higher for the green protein than for the red one, which is reasonable in light of the lower extinction coefficient and fluorescence lifetime for the red protein. “Resonant” switch. For fulfilling the dual requirement of reducing the measurement time and ensuring the good signal-to-noise ratio for precise colocalization, photoactivation should be done at the highest photon-fluxes with yet tolerable photo-bleaching. According to the results of Renz and Wunder (in this issue page 411), the photoactivation efficiency maximizes at a certain photon-flux—boundary of the green and yellow shades—, partially due to the contrasting behavior of activation and photobleaching, depending also on the conditions of illumination (spatial and time fractionation of photon dose). Optimization has been carried out thus far according to the spatial and time fractionation of the activating photon dose. However, there are excitation modes which might be utilized to further improve the present results: polarization modes and excitation by local field such as in FRET or in total internal reflection fluorescence (TIRF). Transitions between the different rotational isomeric states can be evoked by light illuminations, utilizing energy of the photons. A common theme is that interactions of the chromophore groups with their environment—forces and torques exerted by the neighboring amino acids—in the excited state is dramatically altered as compared to the ground state, leading to a transition into a new conformational state. In addition to this passive effect represented by excitation—bond-rearrangements and “photoexcitation- or light-induced rotation (LIR)”—, light might also play a more active role, via its capability of exerting force and torque to the chromophores dictated by the mode of light polarization (linear vs. circular) 12, 16. The large inhomogeneity of evanescent waves, for example, in TIRF illumination makes possible also transferring angular momentum to the chromophores 17. Principally, FRET donors are also capable of exerting force and torque on the acceptor via their local fields—“molecular tweezers”—, which might override thermic motion in critical states of the acceptor, when the other influences exerted by the neighborhood of the acceptor just balance each other 18, 19. Another degree of freedom for optimizing photoactivation might be the time-profile of the activating pulse itself. As the most obvious and important consequence of this work, knowledge of the photoactivation efficiencies of PA-FPs and thus, the fractions of photoactivated proteins will allow the estimation of the real total number of proteins in a sample even when photocativation is incomplete. This could make PALM a reliable single molecule counting technique. Financial support to L.B. for this work was provided by TÁMOP-4.2.2.A-11/1/KONV-2012–0045 project co-financed by the European Union and the European Social Fund, OTKA Bridging Fund support OSTRAT/810/213 by the University of Debrecen; to G.V. by GINOP-2.3.2–15–2016–00026, GINOP-2.3.3–15–2016–00003, and OTKA K103965 by the National Research, Development and Innovation Office, Hungary and TÁMOP-4.2.4.A/2–11/1–2012-0001 “National Excellence Program.” L.B. is wishing to express the appreciation for Imre Péntek (Nagykőrös, Hungary) for a fascinating first introduction into the field of wave polarization.

The effects of donor homo-Förster resonance energy transfer (homo-FRET) taking place in hetero-FRET systems is described in the context of hetero-FRET detection via donor and acceptor fluorescence anisotropies in cell surface receptor clusters. Donor homo-FRET can influence both the efficiency of detection as well as the magnitude of the detectable hetero-FRET. A 4-fold polarized FRET detection scheme-tetrapolarization FRET (4polFRET)-is proposed not only for discriminating the effects of homo-FRET from those of hetero-FRET, but also for correlating homo-associations of the donors and acceptors at different donor-acceptor distances, even beyond the critical Förster distance for hetero-FRET ( R0). The method is based on suppressing homo-FRET at the donor side with red-edge excitation. After the anisotropy effects of physical rotation and homo-FRET were separated by site-selective spectroscopy, the magnitude of the effect of homo-FRET on hetero-FRET has been estimated. It has been found significant, offering a new sensitive technique for detecting conformational dynamics via the homo-FRET mediated component of hetero-FRET, the "homo-FRET enhanced hetero-FRET" or "homo-FRET gate". The method is realizable in flow, as well as in image cytometry equipped with polarization detecting facility.