Theory of photon statistics in single-molecule Förster resonance energy transfer

We present the theory for the distribution of the number of donor and acceptor photons detected in a time bin and the corresponding energy-transfer efficiency distribution obtained from single-molecule Forster resonance energy-transfer measurements. Photon counts from both immobilized and freely diffusing molecules are considered. Our starting point is the joint distribution for the donor and acceptor photons for a system described by an arbitrary kinetic scheme. This is simplified by exploiting the time scale separation between fast fluorescent transitions and slow processes which include conformational dynamics, intersystem conversion to a dark state, and translational diffusion in and out of the laser spot. The fast fluorescent transitions result in a Poisson distribution of the number of photons which is then averaged over slow fluctuations of the local transfer efficiency and the total number of photons. The contribution of various processes to the distribution and the variance of the energy-transfer efficiency are analyzed.     

Beyond Förster resonance energy transfer in linear nanoscale systems

The line dipole approximation is used to investigate analytical corrections to the F?rster energy transfer rate, k, derived via the point dipole approximation. It is shown that that for molecules whose conjugation length, L, is much larger than the separation, R, between molecules the line dipole approximation predicts k ~ (RL)?2 ~ (RN)?2 (where N is the number of conjugated monomer units). This is in contrast to the point dipole approximation, which predicts k ~ L2R?? ~ N2R??.     

Spectral Förster resonance energy transfer detection of protein interactions in surface-supported bilayers

F?rster resonance energy transfer (FRET), a fluorescence detection technique, is often used for sensing molecular interactions in solution and in membranes. Here we show that (1) FRET spectra can be recorded in single bilayers, supported on a surface, and (2) the fluorescein/rhodamine dye pair is an adequate reporter of FRET when spectral detection is used. Thus, measurements pertaining to molecular interactions in membranes can be carried out in supported bilayers. Spectral FRET has advantages over imaging FRET, which monitors only signal amplitudes at certain wavelength. There are also advantages to performing spectral FRET measurements in supported bilayers as compared to free liposomes in suspension. However, the spectral properties of dyes can be altered in an unexpected manner in an ordered bilayer structure on a surface, such that fluorescence detection in surface-supported bilayers is not always trivial.     

The effect of Brownian motion of fluorescent probes on measuring nanoscale distances by Förster resonance energy transfer

F?rster resonance energy transfer (FRET) is a powerful optical technique to determine intra-molecular distances. However, the dye rotational motion and the linker flexibility complicate the relationship between the measured energy transfer efficiency and the distance between the anchoring points of the dyes. In this study, we present a simple model that describes the linker and dye dynamics as diffusion on a sphere. Single-pair energy transfer was treated in the weak excitation limit, photon statistics and scaffold flexibility were ignored, and different time-averaging regimes were considered. Despite the approximations, our model provides new insights for experimental designs and results interpretation in single-molecule FRET. Monte Carlo simulations produced distributions of the inter-dye distance, the dipole orientation factor, κ(2), and the transfer efficiency, E, which were in perfect agreement with independently derived theoretical functions. Contrary to common perceptions, our data show that longer linkers will actually restrict the motion of dye dipoles and hence worsen the isotropic 2∕3 approximation of κ(2). It is also found that the thermal motions of the dye-linker system cause fast and large efficiency fluctuations, as shown by the simulated FRET time-trajectories binned on a microsecond time scale. A fundamental resolution limit of single-molecule FRET measurements emerges around 1-10 μs, which should be considered for the interpretation of data recorded on such fast time scales.     

Förster energy transfer in chlorosomes of green photosynthetic bacteria

Energy transfer properties of whole cells and chlorosome antenna complexes isolated from the green sulfur bacteria Chlorobium limicola (containing bacteriochlorophyll c), Chlorobium vibrioforme (containing bacteriochlorophyll d) and Pelodictyon phaeoclathratiforme (containing bacteriochlorophyll e) were measured. The spectral overlap of the major chlorosome pigment (bacteriochlorophyll c, d or, e) with the bacteriochlorophyll a B795 chlorosome baseplate pigment is greatest for bacteriochlorophyll c and smallest for bacteriochlorophyll e. The absorbance and fluorescence spectra of isolated chlorosomes were measured, fitted to gaussian curves and the overlap factors with B795 calculated. Energy transfer times from the bacteriochlorophyll c, d or e to B795 were measured in whole cells and the results interpreted in terms of the F?rster theory of energy transfer.     

Beyond the Förster formulation for resonance energy transfer: the role of dark states

Resonance Energy Transfer (RET) is investigated in pairs of charge-transfer (CT) chromophores. CT chromophores are an interesting class of π conjugated chromophores decorated with one or more electron-donor and acceptor groups in polar (D-π-A), quadrupolar (D-π-A-π-D or A-π-D-π-A) or octupolar (D(-π-A)(3) or A(-π-D)(3)) structures. Essential-state models accurately describe low-energy linear and nonlinear spectra of CT-chromophores and proved very useful to describe spectroscopic effects of electrostatic interchromophore interactions in multichromophoric assemblies. Here we apply the same approach to describe RET between CT-chromophores. The results are quantitatively validated by an extensive comparison with time-dependent density functional theory (TDDFT) calculations, confirming that essential-state models offer a simple and reliable approach for the calculation of electrostatic interchromophore interactions. This is an important result since it sets the basis for more refined treatments of RET: essential-state models are in fact easily extended to account for molecular vibrations in truly non-adiabatic approaches and to account for inhomogeneous broadening effects due to polar solvation. Optically forbidden (dark) states of quadrupolar and octupolar chromophores offer an interesting opportunity to verify the reliability of the dipolar approximation. In striking contrast with the dipolar approximation that strictly forbids RET towards or from dark states, our results demonstrate that dark states can take an active role in RET with interaction energies that, depending on the relative orientation of the chromophores, can be even larger than those relevant to allowed states. Essential-state models, whose predictions are quantitatively confirmed by TDDFT results, allow us to relate RET interaction energies towards allowed and dark states to the supramolecular symmetry of the RET-pair, offering reliable design strategies to optimize RET-interactions.     

Förster energy transfer from nonexponentially decaying donors

Necessary modifications to the expression for the F?rster energy transfer rate are discussed when fluorescence decay of the donor in the absence of acceptor is nonexponential. Discrete and continuous models of the nonexponentiality are taken into account. No general solution of the problem is found. It is, however, suggested that in many of the biochemical problems the most appropriate modification of the transfer rate can be that which is based on the assumption of the same constant value of the radiative decay rate for all donor molecules. The effect of the assumed form of the F?rster energy transfer rate on the recovered values of the distance distribution and dynamics parameters of some exemplary bichromophoric systems is examined.     

Probing intramolecular Förster resonance energy transfer in a naphthaleneimide-peryleneimide-terrylenediimide-based dendrimer by ensemble and single-molecule fluorescence spectroscopy

We report on the ensemble and single-molecule (SM) dynamics of F?rster resonance energy transfer (FRET) in a multichromophoric rigid polyphenylenic dendrimer (triad) with spectrally different rylene chromophores featuring distinct absorption and emission spectra which cover the whole visible spectral range: a terrylenediimide (TDI) core, four perylenemonoimides (PMIs) attached at the scaffold, and eight naphthalenemonoimides (NMIs) at the rim. For FRET from PMI to TDI taking place with an efficiency of 99.5%, single triad molecules optically excited at 490 nm show fluorescence exclusively from the TDI side in the beginning of their emission. On 360-nm excitation, NMI chromophores transfer their excitation energy either directly or in a stepwise fashion to the core TDI, the latter case involving scaffold-substituted PMIs as intermediate acceptors. Indeed, SM experiments on 360-nm excitation evidence highly efficient FRET from NMI chromophores to the TDI core since individual triad molecules show fluorescence exclusively either from TDI or from an intermediate (oxidized) species but never from PMI. Because PMI and TDI are chromophores with high fluorescence quantum yields and high resistance to photobleaching compared to NMI, 360-nm excitation of a single triad molecule leads to bleaching of NMI chromophores with no chance for PMI to be observed. The spatial positioning and the spectral properties of the chosen rylene chromophores make this multichromophoric system an efficient light collector, able to capture light over the whole visible spectral range and to transfer it finally to the core TDI, the latter releasing it as red fluorescence.     

Förster resonance energy transfer in nanoclusters of InP@ZnS colloidal quantum dots with dodecylamine ligand shells

Förster resonance energy transfer between InP@ZnS hydrophobic colloidal quantum dots of two different sizes has been studied in the closely packed nanoclusters formed spontaneously in an organic solvent upon the addition of a precipitating solvent. The quantum dots had a core@shell structure and were stabilized by dodecylamine ligands.     

Ratiometric pH sensor based on mesoporous silica nanoparticles and Förster resonance energy transfer

Incorporation of a dual-FRET dye pair into mesoporous silica nanoparticles yields sensitive and sensing-range tunable nanosensors with good reversibility that can be used for ratiometric pH measurements under a single-wavelength excitation.     

Manipulation of Förster energy transfer of coupled fluorophores through biotransformation by Pseudomonas resinovorans CA10

An alkyne‐terminated anthracene and azide‐terminated carbazole were joined through a copper‐catalyzed cycloaddition to form a joined donor/acceptor pair. The photonic pair exhibited energy transfer when excited at the peak absorbance of carbazole and fluoresced with an anthracene spectral response. The fluorescent behavior was confirmed as Förster energy transfer (FRET). The lysate of Pseudomonas resinovorans CA10, a member of a predominant group of soil microorganisms that can metabolize a host of substrates, was employed to degrade the pair and alter the luminance spectral characteristics. The FRET was diminished and the corresponding, individual fluorescence of carbazole and anthracene returned. This general approach may find applications in single‐cell metabolic studies and bioactivity assays.     

Single-molecule Förster resonance energy transfer reveals an innate fidelity checkpoint in DNA polymerase I

Enzymatic reactions typically involve complex dynamics during substrate binding, conformational rearrangement, chemistry, and product release. The noncovalent steps provide kinetic checkpoints that contribute to the overall specificity of enzymatic reactions. DNA polymerases perform DNA replication with outstanding fidelity by actively rejecting noncognate nucleotide substrates early in the reaction pathway. Substrates are delivered to the active site by a flexible fingers subdomain of the enzyme, as it converts from an open to a closed conformation. The conformational dynamics of the fingers subdomain might also play a role in nucleotide selection, although the precise role is currently unknown. Using single-molecule F?rster resonance energy transfer, we observed individual Escherichia coli DNA polymerase I (Klenow fragment) molecules performing substrate selection. We discovered that the fingers subdomain actually samples through three distinct conformations--open, closed, and a previously unrecognized intermediate conformation. We measured the overall dissociation rate of the polymerase-DNA complex and the distribution among the various conformational states in the absence and presence of nucleotide substrates, which were either correct or incorrect. Correct substrates promote rapid progression of the polymerase to the catalytically competent closed conformation, whereas incorrect nucleotides block the enzyme in the intermediate conformation and induce rapid dissociation from DNA. Remarkably, incorrect nucleotide substrates also promote partitioning of DNA to the spatially separated 3'-5' exonuclease domain, providing an additional mechanism to prevent misincorporation at the polymerase active site. These results reveal the existence of an early innate fidelity checkpoint, rejecting incorrect nucleotide substrates before the enzyme encloses the nascent base pair.     

Probing the dynamic nature of DNA multilayer films using förster resonance energy transfer

DNA films are of interest for use in a number of areas, including sensing, diagnostics, and as drug/gene delivery carriers. The specific base pairing of DNA materials can be used to manipulate their architecture and degradability. The programmable nature of these materials leads to complex and unexpected structures that can be formed from solution assembly. Herein, we investigate the structure of DNA multilayer films using F?rster resonance energy transfer (FRET). The DNA films are assembled on silica particles by depositing alternating layers of homopolymeric diblocks (polyA(15)G(15) and polyT(15)C(15)) with fluorophore (polyA(15)G(15)-TAMRA) and quencher (polyT(15)C(15)-BHQ2) layers incorporated at predesigned locations throughout the films. Our results show that DNA films are dynamic structures that undergo rearrangement. This occurs when the multilayer films are perturbed during new layer formation through hybridization but can also take place spontaneously when left over time. These films are anticipated to be useful in drug delivery applications and sensing applications.     

Structural variability of nucleosomes detected by single-pair Förster resonance energy transfer: histone acetylation, sequence variation, and salt effects

Nucleosomes were reconstituted from 170 bp long fragments of 5S rDNA and an optimal positioning sequence, the Selex 601, with recombinant histones. In free-solution single pair F?rster resonance energy transfer (spFRET) measurements of the distance between fluorescently labeled bases in the nucleosomal DNA, the samples exhibited structural diversity. The structural heterogeneity correlated with the stability of the complexes and depended on the DNA sequence and histone acetylation. The stability of the nucleosomes was assessed via dilution-driven disruption: histone acetylation decreased nucleosome stability. The spFRET experiments used a new approach for data acquisition and analysis that we term "deliberately detuned detection" (D3). This permits the separation of subpopulations in the samples even for the low-FRET regime characteristic for the linker-DNA labeled nucleosomes. Thus, it became possible to study in more detail histone acetylation- and salt-dependent structural variations using either end- or internally labeled DNAs on the nucleosome. We found that the distance distribution of the fluorophore pairs on the linker DNA ends was much more sensitive to histone acetylation or sequence variation than that of labels on the internal part of the DNA, which was more tightly associated with the histone core. spFRET on freely diffusing nucleosomes allows us therefore to localize the influence of histone modifications and DNA sequence variations on the nucleosome structure and dynamics.     

Long time scale blinking kinetics of cyanine fluorophores conjugated to DNA and its effect on Förster resonance energy transfer

The blinking kinetics of individual Cy5 fluorophores conjugated to DNA are directly measured using single-molecule spectroscopy. Under deoxygenated aqueous conditions, Cy5 fluorescence exhibits spontaneous and reversible on/off fluctuations with a period lasting seconds. This blinking is observed when directly exciting Cy5 with 640 nm light and by Forster resonance energy transfer (FRET). We find that Cy5 blinking is influenced by the proximity of the donor, the structure of the donor, the presence of 514 nm excitation, and FRET. In the context of single-molecule FRET, blinking of the acceptor produces anticorrelated donor-acceptor intensity fluctuations, which can be difficult to discern from variations in the interdye distance. Slow blinking is, in particular, problematic because it overlaps with biologically relevant time scales. By employing an alternating 514640 nm laser excitation scheme, we show that the dark states can be readily resolved and discriminated from FRET distance fluctuations.     

Small-molecule ligands strongly affect the Förster resonance energy transfer between a quantum dot and a fluorescent protein

We report herein the study of F?rster resonance energy transfer (FRET) between a CdSe/ZnS core/shell quantum dot (QD) capped with three different small-molecule ligands, 3-mercaptopropionic acid (MPA), glutathione (GSH), and dihydrolipoic acid (DHLA), and a hexa-histidine (His(6))-tagged fluorescent protein, mCherry (FP). The F?rster radius (R(0)) and the corresponding donor-acceptor distances (r) for each of the QD-FP FRET systems were evaluated by using the F?rster dipole-dipole interaction formula. Interestingly, both the FRET efficiency (E) and r were found to be strongly dependent on the capping small-molecule ligands on the QD surface, where E ≈ 85% was obtained at a FP:QD copy number of 2:1 for the MPA capped QD, while that for the DHLA capped QD was <25% under the same conditions. A molecular model was proposed to explain the possible reasons behind these observations. The dissociation constants (K(d)s) and kinetics of the self-assembled QD-FP systems were also evaluated. Results show that the QD-FP self-assembly process is fast (completes in minutes at low nM concentrations), strong (with K(d) ≈ 1 nM) and positively cooperative (with the Hill coefficient n > 1), suggesting that the QD-His(6)-tagged biomolecule self-assembly is a facile, effective approach for making compact QD-bioconjugates which may have a wide range of sensing and biomedical applications.     

Förster energy transfer in cholesteric mixtures: a new type of phototunable fluorescent material

A new approach to the creation of cholesteric glass‐forming materials with photovariable fluorescent properties is suggested. This approach is based on Förster type energy transfer from a photochemically active donor to a highly fluorescent acceptor. For this purpose, a cholesteric mixture containing two fluorescent dopants based on anthracene (Dianthr) and stilbene (DCM) was prepared and studied. The absorbance peak of DCM molecules overlaps the emission peak of Dianthr. The possibility of using energy transfer in cholesteric mixtures containing a photoactive energy donor capable of photobleaching is demonstrated. It is shown that UV irradiation of planarly oriented films of the mixture leads to photodimerization of the Dianthr dopant. This photoreaction results in a significant decrease in the emission intensity of the DCM dopant. In all cases the emitted light is strongly circularly polarized, and the degree of polarization does not change during photoreaction. Such types of photo‐patternable glass‐forming cholesteric materials combining fluorescent properties, the possibility of energy transfer between two fluorescent dyes and a photoactivity of one fluorescent component, provide new opportunities for optical data recording and storage.