Diffusion-modulated energy transfer and quenching: analysis by numerical integration of diffusion equation in laplace space

Combining Graphical and Analytical Methods with Molecular Simulations To Analyze Time-Resolved FRET Measurements of Labeled Macromolecules Accurately

Förster resonance energy transfer (FRET) measurements from a donor, D, to an acceptor, A, fluorophore are frequently used in vitro and in live cells to reveal information on the structure and dynamics of DA labeled macromolecules. Accurate descriptions of FRET measurements by molecular models are complicated because the fluorophores are usually coupled to the macromolecule via flexible long linkers allowing for diffusional exchange between multiple states with different fluorescence properties caused by distinct environmental quenching, dye mobilities, and variable DA distances. It is often assumed for the analysis of fluorescence intensity decays that DA distances and D quenching are uncorrelated (homogeneous quenching by FRET) and that the exchange between distinct fluorophore states is slow (quasistatic). This allows us to introduce the FRET-induced donor decay, ε_D(t), a function solely depending on the species fraction distribution of the rate constants of energy transfer by FRET, for a convenient joint analysis of fluorescence decays of FRET and reference samples by integrated graphical and analytical procedures. Additionally, we developed a simulation toolkit to model dye diffusion, fluorescence quenching by the protein surface, and FRET. A benchmark study with simulated fluorescence decays of 500 protein structures demonstrates that the quasistatic homogeneous model works very well and recovers for single conformations the average DA distances with an accuracy of < 2%. For more complex cases, where proteins adopt multiple conformations with significantly different dye environments (heterogeneous case), we introduce a general analysis framework and evaluate its power in resolving heterogeneities in DA distances. The developed fast simulation methods, relying on Brownian dynamics of a coarse-grained dye in its sterically accessible volume, allow us to incorporate structural information in the decay analysis for heterogeneous cases by relating dye states with protein conformations to pave the way for fluorescence and FRET-based dynamic structural biology. Finally, we present theories and simulations to assess the accuracy and precision of steady-state and time-resolved FRET measurements in resolving DA distances on the single-molecule and ensemble level and provide a rigorous framework for estimating approximation, systematic, and statistical errors.

p-Cyanophenylalanine and selenomethionine constitute a useful fluorophore-quencher pair for short distance measurements: application to polyproline peptides

The C≡N stretching frequency and fluorescence quantum yield of p-cyanophenylalanine are sensitive to environment. As such, this unnatural amino acid has found broad applications, ranging from studying how proteins fold to determining the local electric field of membranes. Herein, we demonstrate that the fluorescence of p-cyanophenylalanine can be quenched by selenomethionine through an electron transfer process occurring at short distances, thus further expanding its spectroscopic utility. Using this fluorophore-quencher pair, we are able to show that short polyproline peptides (1-4 prolines) are not rigid; instead, they sample a bimodal conformational distribution.

Förster resonance energy transfer and trapping in selected systems: analysis by Monte-Carlo simulation

Monte-Carlo simulation method is described and applied as an efficient tool to analyze experimental data in the presence of energy transfer in selected systems, where the use of analytical approaches is limited or even impossible. Several numerical and physical problems accompanying Monte-Carlo simulation are addressed. It is shown that the Monte-Carlo simulation enables to obtain orientation factor in partly ordered systems and other important energy transfer parameters unavailable directly from experiments. It is shown how Monte-Carlo simulation can predict some important features of energy transport like its directional character in ordered media.

Förster energy transfer from nonexponentially decaying donors

Necessary modifications to the expression for the Förster 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 Förster energy transfer rate on the recovered values of the distance distribution and dynamics parameters of some exemplary bichromophoric systems is examined.

Lateral diffusion coefficients in membranes measured by resonance energy transfer and a new algorithm for diffusion in two dimensions

We describe measurements of lateral diffusion in membranes using resonance energy transfer. The donor was a rhenium (Re) metal-ligand complex lipid, which displays a donor decay time near 3 micros. The long donor lifetime resulted in an ability to measure lateral diffusion coefficient below 10(-8) cm(2)/s. The donor decay data were analyzed using a new numerical algorithm for calculation of resonance energy transfer for donors and acceptors randomly distributed in two dimensions. An analytical solution to the diffusion equation in two dimensions is not known, so the equation was solved by the relaxation method in Laplace space. This algorithm allows the donor decay in the absence of energy transfer to be multiexponential. The simulations show that mutual lateral diffusion coefficients of the donor and acceptor on the order of 10(-8) cm(2)/s are readily recovered from the frequency-domain data with donor decay times on the microsecond timescale. Importantly, the lateral diffusion coefficients and acceptor concentrations can be recovered independently despite correlation between these parameters. This algorithm was tested and verified using the donor decays of a long lifetime rhenium lipid donor and a Texas red-lipid acceptor. Lateral diffusion coefficients ranged from 4.4 x 10(-9) cm(2)/s in 1,2-dimyristoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DMPG) at 10 degrees C to 1.7 x 10(-7) cm(2)/s in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) at 35 degrees C. These results demonstrated the possibility of direct measurements of lateral diffusion coefficients using microsecond decay time luminophores.

Influence of solvent and configuration of residues at positions 2 and 3 on distance and mobility of pharmacophore groups at positions 1 and 4 in cyclic enkephalin analogues

The analgesic activity of opioid peptides is mainly connected with their affinity and selectivity for the mu-receptors. The biological activity of cyclic opioid analogues depends on mutual orientation and conformational freedom of aromatic pharmacophore groups at positions 1 and 4. The distance and distance distributions between chromophores at positions 1 [Phe(p-NO(2)), p-nitrophenylalanine] and 4 [Nal, beta-(2-naphthyl)alanine], which constitute an energy donor-acceptor pair, were calculated based on measured fluorescence intensity decays of a donor (Nal). The influence of the solvent and configuration of the residues at position 2 and 3 on donor-acceptor distance distribution and mobility of pharmacophore groups at position 1 and 4 in cyclic enkephalin analogues are discussed.

Effects of diffusion on energy transfer in solution using a microsecond decay time rhenium metal-ligand complex as the donor

We used resonance energy transfer and frequency-domain fluorometry to measure slow donor to acceptor diffusion in viscous media. The frequency-domain RET data were analyzed using a new numerical algorithm for predicting the donor intensity decay in the presence of diffusion occurring within the donor decay time. By the use of a rhenium metal-ligand complex as a microsecond decay time donor we were able to measure mutual donor-to-acceptor diffusion coefficients as low as 2 × 10-8 cm2/s. The availability of microsecond decay time luminophores and appropriate theory suggests the use of diffusion-enhanced energy transfer for measurement of diffusive processes and structural dynamics in biological systems.

Time-resolved and steady-state fluorescence quenching of N-acetyl-L-tryptophanamide by acrylamide and iodide

We examined the time-resolved and steady-state fluorescence quenching of N-acetyl-L-tryptophanamide (NATA) by acrylamide and iodide, over a range of viscosities in propylene glycol. The quenching of NATA by acrylamide and iodide results in heterogeneity of the intensity decay which increases with the quencher concentration. We attribute the complex decays of NATA to transient effects in diffusion and the nature of the fluorophore-quencher interaction. These data were compared using the phenomenological radiation boundary condition (RBC) and distance-dependent quenching (DDQ) models for collisional quenching. We used global analysis of the time-resolved frequency-domain and steady-state data to select between the models. Consideration of both the frequency-domain and steady state data demonstrate that the quenching rate depends exponentially on the fluorophore-quencher distance, indicating the validity of the DDQ model. The rate constants for acrylamide and iodide quenching, at the constant distance of 5 A, were found to be near 10(13) s-1 and 10(9) s-1, respectively. These rates reflect electron transfer and exchange interactions as the probable quenching mechanisms, respectively.

Distance-Dependent Fluorescence Quenching of p-Bis[2-(5-phenyloxazolyl)]benzene by Various Quenchers

We report results of frequency-domain and steady-state measurements of the fluorescence quenching of p-bis-[2-(5-phenyloxazolyl)]benzene (POPOP) when quenched by bromoform (CHBr3), methyl iodide (CH3I), potassium iodide (KI), 1,2,4-trimethoxybenzene (TMB), or N,N-diethylaniline (DEA). The quenching efficiency of these compounds decreased in the order DEA, TMB, KI, CH3I, CHBr3. In the case of DEA and TMB the measurements clearly confirm the applicability of the exponential distance-dependent quenching (DDQ) model, in which the bimolecular quenching rate k(r) depends exponentially on the fluorophore–quencher separation r, k(r) = ka exp[−(r − a)/re], where a is the distance of closest approach. Simultaneous analysis of the frequency-domain and steady-state data significantly improved resolution of the recovered molecular parameters ka and re. The data for DEA and TMB cannot be satisfactorily fit using either the Smoluchowski or Collins–Kimball radiation boundary condition (RBC) model. The quenching behavior of the less efficient quenchers KI, CH3I, and CHBr3 can be adequately described with both the DDQ and RBC models, but this may be a simple consequence of less efficient quenching. The efficiency of quenching is discussed on the basis of the mechanisms of interaction between the fluorophore and quencher molecules, which involves electron transfer and/or heavy atom effects.

Distance distributions from the tyrosyl to disulfide residues in the oxytocin and [Arg8]-vasopressin measured using frequency-domain fluorescence resonance energy transfer

We have examined the fluorescence intensity decays of oxytocin and [Arg8]-vasopressin resulting from the single tyrosyl residue in each peptide, and the intensity decay of the Asu1,6-analogues in which the disulfide bridge is substituted by a CH2-CH2 bridge. Viscosity-dependent steady state and intensity decay measurements indicated that fluorescence resonance energy transfer (FRET) from tyrosyl phenol to the disulfide bridge is responsible for the decrease in fluorescence relative to the Asu-analogues. The frequency-domain phase and modulation data for the tyrosyl donor were interpreted in terms of fluorescence resonance energy transfer (FRET) to the weakly absorbing disulfide bridge and a distribution of donor-to-acceptor distances. Energy transfer efficiencies were determined from both time-resolved and steady-state measurements. Fitting the frequency-domain phase and modulation data to a Gaussian distance distribution indicated that the average inter-chromophoric distance (Rav) is similar in both compounds, Rav = 7.94 A for oxytocin and Rav = 8.00 A for vasopressin. However, the width of the distance distribution is narrower for vasopression (hw = 2.80 A) than for oxytocin (hw = 3.58 A), which is consistent with restriction of the tyrosine phenol motion due to its stacking wih the Phe3 side chain of vasopressin. Finally, the recovered distance distribution functions are compared with histograms describing the distance between the chromophores during the course of long, in vacuo, molecular dynamics runs using the computer program CHARMm and the QUANTA 3.0 parameters.