A distribution-based method to resolve single-molecule Förster resonance energy transfer observations

We introduce a new approach to analyze single-molecule Fo?rster resonance energy transfer (FRET) data. The method recognizes that FRET efficiencies assumed by traditional ensemble methods are unobservable for single molecules. We propose instead a method to predict distributions of FRET parameters obtained directly from the data. Distributions of FRET rates, given the data, are precisely defined using Bayesian methods and increase the information derived from the data. Benchmark comparisons find that the response time of the new method outperforms traditional methods of averaging. Our approach makes no assumption about the number or distribution of underlying FRET states. The new method also yields information about joint parameter distributions going beyond the standard framework of FRET analysis. For example, the running distribution of FRET means contains more information than any conceivable single measure of FRET efficiency. The method is tested against simulated data and then applied to a pilot-study sample of calmodulin molecules immobilized in lipid vesicles, revealing evidence for multiple dynamical states.     

Vibrational energy transfer and anisotropy decay in liquid water: is the Förster model valid?

Ultrafast pump-probe anisotropy experiments have been performed on liquid H(2)O and D(2)O. In both cases, the anisotropy decay is extremely fast (on the order of 100 or 200 fs) and is presumed due to resonant vibrational energy transfer. The experiments have been interpreted in terms of the Fo?rster theory, wherein the rate constant for intermolecular hopping transport is proportional to the inverse sixth power of the distance between the vibrational chromophores. In particular, the anisotropy decay is assumed to be simply related to the survival probability as calculated with the Fo?rster theory. While the theory fits the data well, and is a reasonable model for these systems, there are several assumptions in the theory that might be suspect for water. Using our mixed quantum/classical model for vibrational spectroscopy and dynamics in liquid water, which agrees well with anisotropy decay experiments on the pure liquids as well as H(2)O/D(2)O mixtures, we critically analyze both the survival probability and anisotropy decay, in order to assess the applicability of the Fo?rster theory.     

Accurate distance determination of nucleic acids via Förster resonance energy transfer: implications of dye linker length and rigidity

In Fo?rster resonance energy transfer (FRET) experiments, the donor (D) and acceptor (A) fluorophores are usually attached to the macromolecule of interest via long flexible linkers of up to 15 ? in length. This causes significant uncertainties in quantitative distance measurements and prevents experiments with short distances between the attachment points of the dyes due to possible dye-dye interactions. We present two approaches to overcome the above problems as demonstrated by FRET measurements for a series of dsDNA and dsRNA internally labeled with Alexa488 and Cy5 as D and A dye, respectively. First, we characterize the influence of linker length and flexibility on FRET for different dye linker types (long, intermediate, short) by analyzing fluorescence lifetime and anisotropy decays. For long linkers, we describe a straightforward procedure that allows for very high accuracy of FRET-based structure determination through proper consideration of the position distribution of the dye and of linker dynamics. The position distribution can be quickly calculated with geometric accessible volume (AV) simulations, provided that the local structure of RNA or DNA in the proximity of the dye is known and that the dye diffuses freely in the sterically allowed space. The AV approach provides results similar to molecular dynamics simulations (MD) and is fully consistent with experimental FRET data. In a benchmark study for ds A-RNA, an rmsd value of 1.3 ? is achieved. Considering the case of undefined dye environments or very short DA distances, we introduce short linkers with a propargyl or alkenyl unit for internal labeling of nucleic acids to minimize position uncertainties. Studies by ensemble time correlated single photon counting and single-molecule detection show that the nature of the linker strongly affects the radius of the dye's accessible volume (6-16 ?). For short propargyl linkers, heterogeneous dye environments are observed on the millisecond time scale. A detailed analysis of possible orientation effects (κ(2) problem) indicates that, for short linkers and unknown local environments, additional κ(2)-related uncertainties are clearly outweighed by better defined dye positions.     

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??.     

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.     

Solvent- and pH-induced self-assembly of cationic meta-linked poly(phenylene ethynylene): effects of helix formation on amplified fluorescence quenching and Förster resonance energy transfer

We reported here the synthesis and characterization of a novel water-soluble, meta-linked poly(phenylene ethynylene) (m-PPE-NEt(2)Me(+)) featuring quaternized side groups. We studied the solvent-induced self-assembly of m-PPE-NEt(2)Me(+) in MeOH/H(2)O solvent mixtures by using UV-vis absorption and fluorescence spectroscopies. The results showed that the polymer folded into a helical conformation and that the extent of helical folding increased with the volume % water in the solvent. This cationic polymer also exhibited unique pH-induced helix formation, which was attributed to the partial neutralization of quaternized side groups at high pH and the meta-links in the main chain of the polymer. Studies on the fluorescence quenching of m-PPE-NEt(2)Me(+) by anthraquinone-2,6-disulfonate (AQS) and Fe(CN)(6)(4-), two small-molecule anionic quenchers with different typical structures, revealed more efficient quenching of helical conformation by AQS than by Fe(CN)(6)(4-). We proposed that the two quenchers most likely interacted with the polymer helix in two different modes; that was, AQS featuring large planar aromatic ring could intercalate within adjacent π-stacked phenylene ethynylene units in the polymer helix, whereas Fe(CN)(6)(4-) mainly bound to the periphery of polymer helix through ion-pair formation. Finally, the results of FRET from the helical polymer to the fluorescein (C*)-labeled polyanions, ssDNA-C* (ssDNA: single-stranded DNA) and dsDNA-C* (dsDNA: double-stranded DNA) also suggested two different modes of interactions. As compared with the FRET to dsDNA-C*, the FRET to ssDNA-C* was slightly more efficient, which was believed to arise from the additional binding of ssDNA-C* with the polymer via intercalation of its exposed hydrophobic bases into the π stack of adjacent phenylene ethynylene units in the polymer helix.     

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.     

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.     

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.     

Intramolecular Förster energy transfer in a dendritic system at the single molecule level

The photophysics of a dendrimer containing four donor chromophores and one acceptor chromophore are studied at the single-molecule level. Upon excitation of the donors exclusive acceptor emission is observed due to efficient F?rster energy transfer. For 70% of the molecules donor emission is observed after bleaching of the acceptor, leading to a reduction of the F?rster energy transfer efficiency. Furthermore, we demonstrate that in this molecular system the donor chromophores do not bleach by a triplet-sensitized photooxidation.     

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.     

Intramolecular directional förster resonance energy transfer at the single-molecule level in a dendritic system

We report on the directional F?rster resonance energy transfer (FRET) process taking place in single molecules of a first (T1P4) and a second (T2P8) generation of a perylenemonoimide (P)-terrylenediimide (T)-based dendrimer in which the chromophores are separated by rigid polyphenylene arms. At low excitation powers, single-molecule detection and spectroscopy of T1P4 and T2P8 dendrimers point to a highly efficient directional FRET from P donors to the central T acceptor, optical excitation at 488 nm resulting in exclusively acceptor emission in the beginning of the detected fluorescence intensity. Donor emission is seen only upon the bleaching of the acceptor. High-resolution time-resolved single-molecule fluorescence data measured with a microchannel plate photomultiplier reveal, for T2P8, a broad range of FRET rates as a result of a broad range of distances and orientations experienced by the donor-acceptor dendrimers when immobilized in a polymer matrix. Single-molecule data from T2P8 on 488 nm excitation are indicative for the presence, after terrylenediimide bleaching, of a P-P excited dimer characterized by a broad emission spectrum peaking around 600 nm and by fluctuating fluorescence decay times. At high excitation powers, single T1P4 and T2P8 molecules display simultaneous emission from both donor and acceptor chromophores. The effect, called "exciton blockade", occurs due to the presence of multiple excitations in a single molecule.     

Exploring Förster electronic energy transfer in a decoupled anthracenyl-based borondipyrromethene (bodipy) dyad

An anthracenyl-Bodipy dyad containing a triazole bridge, that acts to decouple the two units in the ground state, has been synthesised and structurally characterised. Efficient electronic energy transfer occurs from the anthracenyl-based unit to the Bodipy system in toluene in around 12 ps, and becomes faster in solvents of lower refractive index. The rate of electronic energy transfer is discussed in terms of F?rster theory.     

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.     

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.     

Excitation energy transfer mechanism in C-phycocyanin hexamer

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Role of the spacer in the singlet-singlet energy transfer mechanism (Förster vs Dexter) in cofacial bisporphyrins

The cofacial bisporphyrins H4DPS (DPS = 4,6-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]dibenzothiophene), H4DPO (DPO = 4,6-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]dibenzofuran), H4DPX (DPX = 4,5-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]-9,9-dimethylxanthene), H4DPA (DPA = 1,8-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]anthracene), and H4DPB (DPB = 1,8-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]biphenylene) have been monometalated by Zn(OAc)2.2H2O and by GaCl3 to explore the singlet-singlet energy transfer from the photoexcited metal porphyrin center to the linked free base porphyrin. The spectroscopic (UV-vis and fluorescence) and photophysical properties (fluorescence lifetimes, tauF, and quantum yields, phiF) have been investigated at 298 and 77 K in degassed 2-MeTHF for the donor-acceptor systems, (Zn)H2DPS, (Zn)H2DPO, (Zn)H2DPA, (Zn)H2DPX, and (Zn)H2DPB, as well as for the bis-zinc complexes, (Zn)2DPS, (Zn)2DPO, (Zn)2DPX, and (Zn)2DPB, respectively, and the monoporphyrin derivatives, H2P, (Zn)P, and (Ga-OMe)P (P2- = 5-phenyl-2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrin-dianion). The singlet-singlet energy transfer rate constants (KET) were obtained using KET = (1/tauF -1/tauFo), where tauFo is the fluorescence lifetime of the corresponding bis-zinc(II) systems (or (Zn)P and (Ga-OMe)P) where no energy transfer occurs. The tauF value for three bis-zinc(II) compounds varies from 1.69 to 2.01 ns and is 1.84 (at 298 K) and 3.20 ns (at 77 K) for (Ga-OMe)P. In the donor-acceptor bismacrocycles, depending on the spacer and the temperature, the fluorescence lifetimes decrease down to 50-240 ps. The KET values range from approximately 4 to approximately 21 (ns(-1)) and have been analyzed considering both the F?rster and the Dexter mechanisms. Using the C(meso)-C(meso) distance parameters in the calculations, the F?rster and Dexter mechanisms operate for DPS and DPO, and for DPA, DPX, and DPB spacer systems, respectively. The limit distance where one mechanism dominates over the other is estimated to be around 5-6 A.     

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.