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.     

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.     

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.     

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??.     

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.     

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.     

Extending spectrum response of squaraine-sensitized solar cell by Förster resonance energy transfer

To extend the spectral response region of squaraine dye (SQ)-sensitized solar cell, eosin Y (EY) is encapsulated in the SQ-sensitized nanocrystalline thin film. EY is first adsorbed on nanocrystalline TiO₂ thin film (n-TiO₂), then a thin layer of EY contained ZnO (EY-ZnO) is electrodeposited, and SQ dye is finally sensitized to form two dye-sensitized nanocrystalline thin film with a structure of n-TiO₂/EY/EY-ZnO/SQ. There is a perfect spectral overlap between the emission of EY and the absorption of SQ; EY as an energy donor simultaneously transfers both electron and hole to the energy acceptor SQ according to the Förster resonance energy transfer (FRET) process. EY shifts the spectral response edge of SQ-sensitized solar cell toward blue from 550 to 450 nm through the FRET process in this new structure. Two dye-sensitized nanocrystalline thin film demonstrates a significant enhancement in light harvesting and photocurrent generation due to the FRET process. The thickness of the EY-ZnO thin layer and spectral overlap between emission of donor dye and absorption of acceptor dye are two important factors that affect the FRET process between EY and SQ in the structure of n-TiO₂/EY/EY-ZnO/SQ.     

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.     

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 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.     

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.     

Fluorescence resonance energy transfer (FRET) for DNA biosensors: FRET pairs and Förster distances for various dye-DNA conjugates

Fluorescence resonance energy transfer (FRET) between the extrinsic dye labels Cyanine 3 (Cy3), Cyanine 5 (Cy5), Carboxytetramethyl Rhodamine (TAMRA), Iowa Black Fluorescence Quencher (IabFQ), and Iowa Black RQ (IabRQ) has been studied. The F?rster distances for these FRET-pairs in single- and double-stranded DNA conjugates have been determined. In particular, it should be noted that the quantum yield of the donors Cy3 and TAMRA varies between single- and double-stranded DNA. While this alters the F?rster distance for a donor-acceptor pair, this also allows for detection of thermal denaturation events with a single non-intercalating fluorophore. The utility of FRET in the development of nucleic acid biosensor technology is illustrated by using TAMRA and IabRQ as a FRET pair in selectivity experiments. The differential quenching of TAMRA fluorescence by IabRQ in solution has been used to discriminate between 0 and 3 base pair mismatches at 60 degrees C for a 19 base sequence. At room temperature, the quenching of TAMRA fluorescence was not an effective indicator of the degree of base pair mismatch. There appears to be a threshold of duplex stability at room temperature which occurs beyond two base pair mismatches and reverses the observed trend in TAMRA fluorescence prior to that degree of mismatch. When this experimental system is transferred to a glass surface through covalent coupling and organosilane chemistry, the observed trend in TAMRA fluorescence at room temperature is similar to that obtained in bulk solution, but without a threshold of duplex stability. In addition to quenching of fluorescence by FRET, it is believed that several other quenching mechanisms are occurring at the surface.     

Quantum dots as simultaneous acceptors and donors in time-gated Förster resonance energy transfer relays: characterization and biosensing

The unique photophysical properties of semiconductor quantum dot (QD) bioconjugates offer many advantages for active sensing, imaging, and optical diagnostics. In particular, QDs have been widely adopted as either donors or acceptors in F?rster resonance energy transfer (FRET)-based assays and biosensors. Here, we expand their utility by demonstrating that QDs can function in a simultaneous role as acceptors and donors within time-gated FRET relays. To achieve this configuration, the QD was used as a central nanoplatform and coassembled with peptides or oligonucleotides that were labeled with either a long lifetime luminescent terbium(III) complex (Tb) or a fluorescent dye, Alexa Fluor 647 (A647). Within the FRET relay, the QD served as a critical intermediary where (1) an excited-state Tb donor transferred energy to the ground-state QD following a suitable microsecond delay and (2) the QD subsequently transferred that energy to an A647 acceptor. A detailed photophysical analysis was undertaken for each step of the FRET relay. The assembly of increasing ratios of Tb/QD was found to linearly increase the magnitude of the FRET-sensitized time-gated QD photoluminescence intensity. Importantly, the Tb was found to sensitize the subsequent QD-A647 donor-acceptor FRET pair without significantly affecting the intrinsic energy transfer efficiency within the second step in the relay. The utility of incorporating QDs into this type of time-gated energy transfer configuration was demonstrated in prototypical bioassays for monitoring protease activity and nucleic acid hybridization; the latter included a dual target format where each orthogonal FRET step transduced a separate binding event. Potential benefits of this time-gated FRET approach include: eliminating background fluorescence, accessing two approximately independent FRET mechanisms in a single QD-bioconjugate, and multiplexed biosensing based on spectrotemporal resolution of QD-FRET without requiring multiple colors of QD.     

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.     

Interaction of an antituberculosis drug with nano-sized cationic micelle: Förster resonance energy transfer from dansyl to rifampicin in the microenvironment

In this contribution, we report studies on the interaction of an antituberculosis drug rifampicin (RF) in a macromolecular assembly of CTAB with an extrinsic fluorescent probe, dansyl chloride (DC). The absorption spectrum of the drug RF has been employed to study Förster resonance energy transfer (FRET) from DC, bound to the CTAB micelle using picosecond resolved fluorescence spectroscopy. We have applied a kinetic model developed by Tachiya to understand the kinetics of energy transfer and the distribution of acceptor (RF) molecules around the donor (DC) molecules in the micellar surface with increasing quencher concentration. The mean number of RF molecules associated with the micelle increases from 0.24 at 20 μm RF concentration to 1.5 at 190 μm RF concentration and consequently the quenching rate constant (k_q) due to the acceptor (RF) molecules increases from 0.23 to 0.75 ns^?1 at 20 and 190 μm RF concentration, respectively. However, the mean number of the quencher molecule and the quenching rate constant does not change significantly beyond a certain RF concentration (150 μm ), which is consistent with the results obtained from time resolved FRET analysis. Moreover, we have explored the diffusion controlled FRET between DC and RF, using microfluidics setup, which reveals that the reaction pathway follows one‐step process.