The orientation parameter for energy transfer in restricted geometries including block copolymer interfaces: a Monte Carlo study

We describe Monte Carlo simulations of resonance energy transfer (RET) experiments for immobile donor (D) and acceptor (A) dyes confined to planar, cylindrical, and spherical restricted geometries. We compare values of the quantum efficiency (PhiET) evaluated through consideration of individual donor-acceptor pairs, with values calculated assuming a pre-averaged value of the orientation parameter /kappa/2 = 0.476 appropriate for infinite three dimensional (3D) space. For dyes confined to restricted geometries where the length scale of the confining dimension is less than or equal to the F?rster radius R0, the coupling of the orientation parameter and the donor-acceptor distance becomes noticeable. Values of Phi(ET) obtained by proper consideration of the orientation parameter are smaller than those calculated using /kappa/2 = 0.476. We use this Monte Carlo method to reanalyze the fluoresce decay measured from dye-labeled poly(isoprene-b-methyl methacrylate) diblock copolymer with lamellar structure,(1) from which the interface thickness for PI-PMMA lamella can be retrieved. We found the retrieved interface thickness is sensitive to the choice of dipole orientation. If all dipoles in the confined polymer interface have a random orientation, the value of interface thickness was found to be 0.9 +/- 0.2 nm through consideration of individual dipole orientations. Assumption of /kappa/2 = 0.476 in the FRET calculations leads to a larger value of interface thickness (1.3 +/- 0.2 nm) due to the neglect of the coupling between dipole orientation and D-A distance for the dyes confined to lamellar interfaces.     

Two-dimensional fluorescence resonance energy transfer as a probe for protein folding: a theoretical study

We describe a two-dimensional (2D), four-color fluorescence resonance energy transfer (FRET) scheme, in which the conformational dynamics of a protein is followed by simultaneously observing the FRET signal from two different donor-acceptor pairs. For a general class of models that assume Markovian conformational dynamics, we relate the properties of the emission correlation functions to the rates of elementary kinetic steps in the model. We further use a toy folding model that treats proteins as chains with breakable cross-links to examine the relationship between the cooperativity of folding and FRET data and to establish what additional information about the folding dynamics can be gleaned from 2D, as opposed to one-dimensional FRET experiments. We finally discuss the potential advantages of the four-color FRET over the three-color FRET technique.     

Time-resolved studies of charge recombination in the pyrene/TCNQ charge-transfer crystal: evidence for tunneling

Previous studies of solid-state tetracyanobenzene-based donor-acceptor complexes showed that these materials were highly susceptible to both laser and mechanical damage that complicated the analysis of their electron-transfer kinetics. In this paper, we characterize the optical properties of a pyrene/tetracyanoquinodimethane charge-transfer crystal that is much more robust than the tetracyanobenzene compounds. This donor-acceptor complex has a charge-transfer absorption that extends into the near-infrared, rendering the crystal black. We use time-resolved fluorescence and diffuse reflectance transient absorption to study its dynamics after photoexcitation. We show that the initially excited charge-transfer state undergoes a rapid, monoexponential decay with a lifetime of 290 ps at room temperature. There is no evidence for any long-lived intermediate or dark states; therefore, this decay is attributed to charge recombination back to the ground state. Fluorescence lifetime measurements demonstrate that this process becomes temperature-independent below 60 K, indicative of a thermally activated tunneling mechanism. The subnanosecond charge recombination makes this low-band-gap donor-acceptor material a poor candidate for generating long-lived electron-hole pairs.     

FRET Enhancement in Aluminum Zero‐Mode Waveguides

Zero‐mode waveguides (ZMWs) can confine light into attoliter volumes, which enables single molecule fluorescence experiments at physiological micromolar concentrations. Of the fluorescence spectroscopy techniques that can be enhanced by ZMWs, Förster resonance energy transfer (FRET) is one of the most widely used in life sciences. Combining zero‐mode waveguides with FRET provides new opportunities to investigate biochemical structures or follow interaction dynamics at micromolar concentrations with single‐molecule resolution. However, prior to any quantitative FRET analysis on biological samples, it is crucial to establish first the influence of the ZMW on the FRET process. Here, we quantify the FRET rates and efficiencies between individual donor–acceptor fluorophore pairs that diffuse into aluminum zero‐mode waveguides. Aluminum ZMWs are important structures thanks to their commercial availability and the large amount of literature that describe their use for single‐molecule fluorescence spectroscopy. We also compared the results between ZMWs milled in gold and aluminum, and found that although gold has a stronger influence on the decay rates, the lower losses of aluminum in the green spectral region provide larger fluorescence brightness enhancement factors. For both aluminum and gold ZMWs, we observed that the FRET rate scales linearly with the isolated donor decay rate and the local density of optical states. Detailed information about FRET in ZMWs unlocks their application as new devices for enhanced single‐molecule FRET at physiological concentrations.     

Three-dimensional orientational colocalization of individual donor--acceptor pairs

We report on the determination of the three-dimensional orientation of the donor and acceptor transition dipoles in individual fluorescence resonance energy transfer (FRET) pairs by means of scanning optical microscopy with annular illumination. Knowledge of the mutual orientation of the donor and acceptor dipole is mandatory for reliable distance determination based on FRET efficiency measurements. In our model system perylenediimide as the donor and terryelenediimide as the acceptor are coupled via a stiff p-terphenyl linker. The absorption dipoles of the donor and acceptor are selectively addressed by the 488 nm and 647 line of an Ar/Kr mixed gas laser, respectively. A clear deviation from collinearity is observed with a distribution of misalignment angles peaked around 22 degrees.     

Using molecular dynamics and quantum mechanics calculations to model fluorescence observables

We provide a critical examination of two different methods for generating a donor-acceptor electronic coupling trajectory from a molecular dynamics (MD) trajectory and three methods for sampling that coupling trajectory, allowing the modeling of experimental observables directly from the MD simulation. In the first coupling method we perform a single quantum-mechanical (QM) calculation to characterize the excited state behavior, specifically the transition dipole moment, of the fluorescent probe, which is then mapped onto the configuration space sampled by MD. We then utilize these transition dipoles within the ideal dipole approximation (IDA) to determine the electronic coupling between the probes that mediates the transfer of energy. In the second method we perform a QM calculation on each snapshot and use the complete transition densities to calculate the electronic coupling without need for the IDA. The resulting coupling trajectories are then sampled using three methods ranging from an independent sampling of each trajectory point (the independent snapshot method) to a Markov chain treatment that accounts for the dynamics of the coupling in determining effective rates. The results show that the IDA significantly overestimates the energy transfer rate (by a factor of 2.6) during the portions of the trajectory in which the probes are close to each other. Comparison of the sampling methods shows that the Markov chain approach yields more realistic observables at both high and low FRET efficiencies. Differences between the three sampling methods are discussed in terms of the different mechanisms for averaging over structural dynamics in the system. Convergence of the Markov chain method is carefully examined. Together, the methods for estimating coupling and for sampling the coupling provide a mechanism for directly connecting the structural dynamics modeled by MD with fluorescence observables determined through FRET experiments.     

Protein structure and dynamics from single-molecule fluorescence resonance energy transfer

The pros and cons of single-molecule vs ensemble-averaged fluorescence resonance energy transfer (FRET) experiments, performed on proteins, are explored with the help of Langevin dynamics simulations. An off-lattice model of the polypeptide chain is employed, which gives rise to a well-defined native state and two-state folding kinetics. A detailed analysis of the distribution of the donor-acceptor distance is presented at different points along the denaturation curve, along with its dependence on the averaging time window. We show that unique information on the correlation between structure and dynamics, which can only be obtained from single-molecule experiments, is contained in the correlation between the donor-acceptor distance and its displacement. The latter is shown to provide useful information on the free energy landscape of the protein, which is complementary to that obtained from the distribution of donor-acceptor distances.     

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.     

Theoretical investigation of electronic excitation energy transfer in bichromophoric assemblies

Electronic excitation energy transfer (EET) rates in rylene diimide dyads are calculated using second-order approximate coupled-cluster theory and time-dependent density functional theory. We investigate the dependence of the EET rates on the interchromophoric distance and the relative orientation and show that Forster theory works quantitatively only for donor-acceptor separations larger than roughly 5 nm. For smaller distances the EET rates are over- or underestimated by Forster theory depending on the respective orientation of the transition dipole moments of the chromophores. In addition to the direct transfer rates we consider bridge-mediated transfer originating from oligophenylene units placed between the chromophores. We find that the polarizability of the bridge significantly enhances the effective interaction. We compare our calculations to single molecule experiments on two types of dyads and find reasonable agreement between theory and experiment.     

A semiempirical approach to the intra-phycocyanin and inter-phycocyanin fluorescence resonance energy-transfer pathways in phycobilisomes

A semiempirical methodology to model the intra-phycocyanin and inter-phycocyanin fluorescence resonance energy-transfer (FRET) pathways in the rods of the phycobilisomes (PBSs) from Fremyella diplosiphon is presented. Using the F?rster formulation of FRET and combining experimental data and PM3 calculation of the dipole moments of the aromatic portions of the chromophores, transfer constants between pairs of chromophores in the phycocyanin (PC) structure were obtained. Protein docking of two PC hexamers was used to predict the optimal distance and axial rotation angle for the staked PCs in the PBSs' rods. Using the distance obtained by the docking process, transfer constants between pairs of chromophores belonging to different PC hexamers were calculated as a function of the angle of rotation. We show that six preferential FRET pathways within the PC hexameric ring and 15 pathways between hexamers exist, with transfer constants consistent with experimental results. Protein docking predicted the quaternary structure for PCs in rods with inter-phycocyanin distance of 55.6 A and rotation angle of 20.5 degrees . The inter-phycocyanin FRET constant between chromophores at positions beta(155) is maximized at the rotation angle predicted by docking revealing the crucial role of this specific inter-phycocyanin channel in defining the complete set of FRET pathways in the system.     

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.     

Through‐Space Conjugated Molecular Wire Comprising Three π‐Electron Systems

A [2.2]paracyclophane‐based through‐space conjugated oligomer comprising three π‐electron systems was designed and synthesized. The arrangement of three π‐conjugated systems in an appropriate order according to the energy band gap resulted in efficient unidirectional photoexcited energy transfer by the Förster mechanism. The energy transfer efficiency and rate constants were estimated to be >0.999 and >10¹² s^?1, respectively. The key point for the efficient energy transfer is the orientation of the transition dipole moments. The time‐dependent density functional theory (TD‐DFT) studies revealed the transition dipole moments of each stacked π‐electron system; each dipole moment was located on the long axis of each stacked π‐electron system. This alignment of the dipole moments is favorable for fluorescence resonance energy transfer (FRET).     

Fluorescence resonance energy transfer in dye-labeled DNA

We present the results of molecular modeling of dye-labeled, double-stranded DNA. The structural information obtained from the simulations are used as input to an analysis of energy transfer in this system. The simulations reveal the nature of the interaction between a pair of fluorophores and DNA. The donor, tetramethylrhodamine, TMR, attached to the 5′-end of DNA with a six-carbon tether, interacts primarily with DNA's minor groove, but occasionally stacks against the DNA base pairs. The acceptor, Cy5, attached to the opposite strand at positions n (n = 7, 12, 14, 16, 19, 24, 27), binds in the major groove in two distinct locations on the upper and lower part of the groove. We analyzed in detail the dye-to-dye distances, dipole orientation factors and fluorescence resonance energy transfer (FRET) rates. Tests of the validity of the Förster model were conducted using the transition density cube (TDC) method, which provides the exact Coulombic interaction within a certain model chemistry. Our studies show that the use of long tethers does not guarantee rotational freedom of the dyes, as intended in the experiments. Instead, the tethers allow Cy5 to bind in two different geometries, which causes a large uncertainty in the dye-to-dye distances. Our results also show significant fluctuation in the orientation factor, κ², which, together with uncertainty in dye-to-dye distances, cause considerable uncertainty in interpreting FRET measurements. We suggest that molecular modeling, combined with the TDC method, provides a useful tool in designing and interpreting FRET experiments.     

THE ORIENTATION OF THE TRANSITION DIPOLE MOMENTS OF CHLOROPHYLL a and PHEOPHYTIN a IN THEIR MOLECULAR FRAME

Abstract— In this paper we describe the determination of the orientation of the absorption and emission transition dipoles of chlorophyll a and pheophytin a in their molecular frame. For this purpose we have embedded the pigments in anhydrous nitrocellulose films with a concentration of 2 × 10^-7 mol/g. We have shown previously that under these conditions the pigments are in a purely monomeric state, are distributed uniformly both before and after stretching and that no intermolecular energy transfer among the molecules takes place.
Using a combination of steady-state anisotropy experiments on unstretched films and angle-resolved fluorescence depolarization measurements on stretched films, we obtain the orientation of the transition dipole moments of both pigments in their molecular frame and the orientational distribution function of the molecules relative to the stretching direction of the film.
The steady-state anisotropy measurements indicate that chlorophyll a has two distinct emission dipole moments and that excitation in the Soret-region results in simultaneous excitation of two or more absorption transition dipole moments. On the other hand, excitation in the Q_Y-band involves only a single dipole moment. The directions of the transition dipole moments in the molecular frame are obtained from the angle-resolved measurements. Pheophytin a also exhibits two emission dipole moments, but the angle between them is much smaller than that between the corresponding dipoles for chlorophyll a . As a consequence the dipole moments contributing to the Soret-region could not be resolved and only an effective absorption transition dipole moment in the Soret-region is extracted.     

Testing the use of molecular dynamics to simulate fluorophore motions and FRET

Fluorescence resonance energy transfer (FRET) is commonly used to determine the proximity of fluorophores, but usually many assumptions are required to gain a quantitative relationship between the likelihood of energy transfer and fluorophore separation. Molecular Dynamics (MD) simulations provide one way of checking these assumptions, but before using simulations to study complex systems it is important to make sure that they can correctly model the motions of fluorophores and the likely FRET efficiency in a simple system. Here we simulate a well characterised situation of independent fluorophores in solution so that we can compare the predictions with expected values. Our simulations reproduce the experimental fluorescence anisotropy of Alexafluor488 and predict that of AlexaFluor568. At the ensemble level we are able to reproduce the expected isotropic and dynamic motion of the fluorophores as well as the FRET efficiency of the system. At the level of single donor-acceptor pairs, however, very long simulations are required to adequately sample the translational motion of the fluorophores and more surprisingly also the rotational motion. Our studies demonstrate how MD simulations can be used in more complex systems to check if the dynamic orientation averaging regime applies, if the fluorophores have isotropic orientational motion, to calculate the likely values of the orientation factor κ(2) and to determine the FRET efficiency of the system in both dynamic and static orientational averaging regimes. We also show that it is possible in some situations to create system specific relationships between FRET efficiency and fluorophore separation that can be used to interpret experimental data and find any correlations between κ(2) and separation that may influence distance measurements.     

Computer simulation to investigate the FRET application in DNA hybridization systems

Molecular dynamics (MD) and quantum mechanics (QM) were used to investigate fluorescence resonance energy transfer (FRET) between coumarin and ethidium in two Mergny's DNA hybridization systems. By combining the transition dipoles calculated by the quantum semi-empirical method and the conformations of the FRET probes collected by MD, FRET efficiencies were derived from the F?rster equation at five temperatures from 273 K to 313 K. The plotted efficiencies were compared with Mergny's experiments, and showed good agreement. The simulated orientation factor and isotropically averaged orientation factor were compared, and the results demonstrated that the assumption of isotropic orientations is invalid when FRET probes are close to each other. The first order kinetic assumptions were also used to calculate the transfer efficiencies, and the results show that this D-A FRET process approximates the first order kinetic reactions.     

Characterization of a single molecule DNA switch in free solution

We have studied a donor-acceptor fluorophore-labeled DNA switch where the acceptor is Alexa-647, a carbocyanine dye, in solution at the single molecule level to elucidate the fluorescence switching mechanism. The acceptor, which is in an initial high fluorescence trans state, undergoes a photoisomerization reaction resulting in two additional states during its sub-millisecond transit across the probe volume. These two states are assigned to a nonfluorescent triplet trans state that strongly quenches the donor emission and a singlet cis state that blocks the fluorescence resonance energy transfer (FRET) pathway and gives rise to donor-only fluorescence. The formation of these states is faster than the transit time, so that all three states are approximately equally populated under our experimental conditions. The acceptor dye can stick to the DNA in all these states, with the rate of unsticking determining the rate of isomerization into the other states. Measurement of the rate of change of the FRET signal therefore provides information about the fluorophore-DNA intramolecular dynamics. These results explain the large zero peak in the proximity ratio, often seen in single molecule FRET experiments, and suggest that photoinduced effects may be important in single molecule FRET experiments using carbocyanine dyes. They also suggest that for fast photoinduced switching the interactions of the acceptor dye with the DNA and other surfaces should be prevented.     

The ultrafast dynamics and nonlinear optical properties of tribranched styryl derivatives based on 1,3,5-triazine

By using the femtosecond laser spectroscopic techniques, we have studied the ultrafast response and the nonlinear optical properties of three molecules with donor-acceptor structure (denoted as T01, T02, and T03). Two-photon absorption (2PA) cross sections measured by the open aperture Z-scan technique were determined to be 77, 90, and 410 GM for T01, T02, and T03, respectively. The relaxation dynamics of the excited states were measured by two-color femtosecond pump-probe and time-resolved photoluminescence (PL) experiments. By changing the solvent from chloroform (CHCl3) to dimethyl sulfoxide (DMSO), the transient dynamics was found changed significantly and the decay time of PL emission decreased dramatically because DMSO with large dipole moment accelerates the cross-transfer process and the nonradiative process in the molecules.     

Crossover from superexchange to hopping as the mechanism for photoinduced charge transfer in DNA hairpin conjugates

The mechanism and dynamics of photoinduced charge separation and charge recombination have been investigated in synthetic DNA hairpins possessing donor and acceptor stilbenes separated by one to seven A:T base pairs. The application of femtosecond broadband pump-probe spectroscopy, nanosecond transient absorption spectroscopy, and picosecond fluorescence decay measurements permits detailed analysis of the formation and decay of the stilbene acceptor singlet state and of the charge-separated intermediates. When the donor and acceptor are separated by a single A:T base pair, charge separation occurs via a single-step superexchange mechanism. However, when the donor and acceptor are separated by two or more A:T base pairs, charge separation occurs via a multistep process consisting of hole injection, hole transport, and hole trapping. In such cases, hole arrival at the electron donor is slower than hole injection into the bridging A-tract. Rate constants for charge separation (hole arrival) and charge recombination are dependent upon the donor-acceptor distance; however, the rate constant for hole injection is independent of the donor-acceptor distance. The observation of crossover from a superexchange to a hopping mechanism provides a "missing link" in the analysis of DNA electron transfer and requires reevaluation of the existing literature for photoinduced electron transfer in DNA.     

Theory of resonance energy transfer involving nanocrystals: the role of high multipoles

A theory for the fluorescence resonance energy transfer (FRET) between a pair of semiconducting nanocrystal quantum dots is developed. Two types of donor-acceptor couplings for the FRET rate are described: dipole-dipole (d-d) and the dipole-quadrupole (d-q) couplings. The theory builds on a simple effective mass model that is used to relate the FRET rate to measureable quantities such as the nanocrystal size, fundamental gap, effective mass, exciton radius, and optical permittivity. We discuss the relative contribution to the FRET rate of the different multipole terms, the role of strong to weak confinement limits, and the effects of nanocrystal sizes.