Diffusion-Enhanced Förster Resonance Energy Transfer in Flexible Peptides: From the Haas-Steinberg Partial Differential Equation to a Closed Analytical Expression.

In the huge field of polymer structure and dynamics, including intrinsically disordered peptides, protein folding, and enzyme activity, many questions remain that cannot be answered by methodology based on artificial intelligence, X-ray, or NMR spectroscopy but maybe by fluorescence spectroscopy. The theory of Förster resonance energy transfer (FRET) describes how an optically excited fluorophore transfers its excitation energy through space to an acceptor moiety-with a rate that depends on the distance between donor and acceptor. When the donor and acceptor moiety are conjugated to different sites of a flexible peptide chain or any other linear polymer, the pair could in principle report on chain structure and dynamics, on the site-to-site distance distribution, and on the diffusion coefficient of mutual site-to-site motion of the peptide chain. However, the dependence of FRET on distance distribution and diffusion is not defined by a closed analytical expression but by a partial differential equation (PDE), by the Haas-Steinberg equation (HSE), which can only be solved by time-consuming numerical methods. As a second complication, time-resolved FRET measurements have thus far been deemed necessary. As a third complication, the evaluation requires a computationally demanding but indispensable global analysis of an extended experimental data set. These requirements have made the method accessible to only a few experts. Here, we show how the Haas-Steinberg equation leads to a closed analytical expression (CAE), the Haas-Steinberg-Jacob equation (HSJE), which relates a diffusion-diagnosing parameter, the effective donor-acceptor distance, to the augmented diffusion coefficient, J, composed of the diffusion coefficient, D, and the photophysical parameters that characterize the used FRET method. The effective donor-acceptor distance is easily retrieved either through time-resolved or steady-state fluorescence measurements. Any global fit can now be performed in seconds and minimizes the sum-of-square difference between the experimental values of the effective distance and the values obtained from the HSJE. In summary, the HSJE can give a decisive advantage in applying the speed and sensitivity of FRET spectroscopy to standing questions of polymer structure and dynamics.

Method-Unifying View of Loop-Formation Kinetics in Peptide and Protein Folding.

Protein folding can be described as a probabilistic succession of events in which the peptide chain forms loops closed by specific amino acid residue contacts, herein referred to as loop nodes. To measure loop rates, several photophysical methods have been introduced where a pair of optically active probes is incorporated at selected chain positions and the excited probe undergoes contact quenching (CQ) upon collision with the second probe. The quenching mechanisms involved triplet-triplet energy transfer, photoinduced electron transfer, and collision-induced fluorescence quenching, where the fluorescence of Dbo, an asparagine residue conjugated to 2,3-diazabicyclo[2.2.2]octane, is quenched by tryptophan. The discrepancy between the loop rates afforded from these three CQ techniques has, however, remained unresolved. In analyzing this discrepancy, we now report two short-distance FRET methods where Dbo acts as an energy acceptor in combination with tryptophan and naphtylalanine, two donors with largely different fluorescence lifetimes of 1.3 and 33 ns, respectively. Despite the different quenching mechanisms, the rates from FRET and CQ methods were, surprisingly, of comparable magnitude. This combination of FRET and CQ data led to a unifying physical model and to the conclusion that the rate of loop formation in folding reactions varies not only with the kind and number of residues that constitute the chain but also in particular with the size and properties of the residues that constitute the loop node.

Two Orders of Magnitude Variation of Diffusion-Enhanced Förster Resonance Energy Transfer in Polypeptide Chains.

A flexible peptide chain displays structural and dynamic properties that correspond to its folding and biological activity. These properties are mirrored in intrachain site-to-site distances and diffusion coefficients of mutual site-to-site motion. Both distance distribution and diffusion determine the extent of Förster resonance energy transfer (FRET) between two sites labeled with a FRET donor and acceptor. The relatively large Förster radii of traditional FRET methods (R0 > 20 Å) lead to a fairly low contribution of diffusion. We introduced short-distance FRET (sdFRET) where Dbo, an asparagine residue conjugated to 2,3-diazabicyclo[2.2.2]octane, acts as acceptor paired with donors, such as naphtylalanine (NAla), tryptophan, 5-l-fluorotryptophan, or tyrosine. The Förster radii are always close to 10 Å, which makes sdFRET highly sensitive to diffusional motion. We recently found indications that the FRET enhancement caused by diffusion depends symmetrically on the product of the radiative fluorescence lifetime of the donor and the diffusion coefficient. In this study, we varied this product by two orders of magnitude, using both donors of different lifetime, NAla and FTrp, as well as a varying viscogen concentration, to corroborate this statement. We demonstrate the consequences of this relationship in evaluating the impact of viscogenic coadditives on peptide dimensions.

Coulomb repulsion in short polypeptides.

Coulomb repulsion between like-charged side chains is presently viewed as a major force that impacts the biological activity of intrinsically disordered polypeptides (IDPs) by determining their spatial dimensions. We investigated short synthetic models of IDPs, purely composed of ionizable amino acid residues and therefore expected to display an extreme structural and dynamic response to pH variation. Two synergistic, custom-made, time-resolved fluorescence methods were applied in tandem to study the structure and dynamics of the acidic and basic hexapeptides Asp6, Glu6, Arg6, Lys6, and His6 between pH 1 and 12. (i) End-to-end distances were obtained from the short-distance Förster resonance energy transfer (sdFRET) from N-terminal 5-fluoro-l-tryptophan (FTrp) to C-terminal Dbo. (ii) End-to-end collision rates were obtained for the same peptides from the collision-induced fluorescence quenching (CIFQ) of Dbo by FTrp. Unexpectedly, the very high increase of charge density at elevated pH had no dynamical or conformational consequence in the anionic chains, neither in the absence nor in the presence of salt, in conflict with the common view and in partial conflict with accompanying molecular dynamics simulations. In contrast, the cationic peptides responded to ionization but with surprising patterns that mirrored the rich individual characteristics of each side chain type. The contrasting results had to be interpreted, by considering salt screening experiments, N-terminal acetylation, and simulations, in terms of an interplay of local dielectric constant and peptide-length dependent side chain charge-charge repulsion, side chain functional group solvation, N-terminal and side chain charge-charge repulsion, and side chain-side chain as well as side chain-backbone interactions. The common picture that emerged is that Coulomb repulsion between water-solvated side chains is efficiently quenched in short peptides as long as side chains are not in direct contact with each other or the main chain.

Chemosensing ensembles for monitoring biomembrane transport in real time.

The efficacy of drugs and biomolecules relies on their ability to pass through the bilayer. The development of methods to directly and sensitively monitor these membrane transport processes has remained an experimental challenge. A macrocyclic host (p-sulfonatocalix[4]arene or cucurbit[7]uril) and a fluorescent dye (lucigenin or berberine) are encapsulated as a chemosensing ensemble inside liposomes, which allows for a direct, real-time fluorescence monitoring of the passage of unlabeled bioorganic analytes. This in vitro assay is transferable to different channel proteins and analytes, has potential for fluorescence-based screening, e.g., of channel modulators, and yields the absolute kinetics of translocation. Using this new biophysical method, we observed for the first time direct rapid translocation of protamine, an antimicrobial peptide, through the bacterial transmembrane protein OmpF.

Diffusion-enhanced Förster resonance energy transfer and the effects of external quenchers and the donor quantum yield.

The structural and dynamic properties of a flexible peptidic chain codetermine its biological activity. These properties are imprinted in intrachain site-to-site distances as well as in diffusion coefficients of mutual site-to-site motion. Both distance distribution and diffusion determine the extent of Förster resonance energy transfer (FRET) between two chain sites labeled with a FRET donor and acceptor. Both could be obtained from time-resolved FRET measurements if their individual contributions to the FRET efficiency could be systematically varied. Because the FRET diffusion enhancement (FDE) depends on the donor-fluorescence lifetime, it has been proposed that the FDE can be reduced by shortening the donor lifetime through an external quencher. Benefiting from the high diffusion sensitivity of short-distance FRET, we tested this concept experimentally on a (Gly-Ser)(6) segment labeled with the donor/acceptor pair naphthylalanine/2,3-diazabicyclo[2.2.2]oct-2-ene (NAla/Dbo). Surprisingly, the very effective quencher potassium iodide (KI) had no effect at all on the average donor-acceptor distance, although the donor lifetime was shortened from ca. 36 ns in the absence of KI to ca. 3 ns in the presence of 30 mM KI. We show that the proposed approach had to fail because it is not the experimentally observed but the radiative donor lifetime that controls the FDE. Because of that, any FRET ensemble measurement can easily underestimate diffusion and might be misleading even if it employs the Haas-Steinberg diffusion equation (HSE). An extension of traditional FRET analysis allowed us to evaluate HSE simulations and to corroborate as well as generalize the experimental results. We demonstrate that diffusion-enhanced FRET depends on the radiative donor lifetime as it depends on the diffusion coefficient, a useful symmetry that can directly be applied to distinguish dynamic and structural effects of viscous cosolvents on the polymer chain. We demonstrate that the effective FRET rate and the recovered donor-acceptor distance depend on the quantum yield, most strongly in the absence of diffusion, which has to be accounted for in the interpretation of distance trends monitored by FRET.

Early closure of a long loop in the refolding of adenylate kinase: a possible key role of non-local interactions in the initial folding steps.

Most globular protein chains, when transferred from high to low denaturant concentrations, collapse instantly before they refold to their native state. The initial compaction of the protein molecule is assumed to have a key effect on the folding pathway, but it is not known whether the earliest structures formed during or instantly after collapse are defined by local or by non-local interactions--that is, by secondary structural elements or by loop closure of long segments of the protein chain. Stable closure of one or several long loops can reduce the chain entropy at a very early stage and can prevent the protein from following non-productive pathways whose number grows exponentially with the length of the protein chain. In Escherichia coli adenylate kinase (AK), about seven long loops define the topology of the native structure. We selected four loop-forming sections of the chain and probed the time course of loop formation during refolding of AK. We labeled the termini of the loop segments with tryptophan and cysteine-5-amidosalicylic acid. This donor-acceptor pair of probes used with fluorescence resonance excitation energy transfer spectroscopy (FRET) is suitable for detecting very short distances and thus is able to distinguish between random and specific compactions. Refolding of AK was initiated by stopped-flow mixing, followed simultaneously by donor and acceptor fluorescence, and analyzed in terms of energy transfer efficiency and distance. In the collapsed state of AK, observed after the 5-ms dead time of the instrument, one of the selected segments shows a native-like separation of its termini; it forms a loop already in the collapsed state. A second segment that includes the first but is longer by 15 residues shows an almost native-like separation of its termini. In contrast, a segment that is shorter but part of the second segment shows a distance separation of its termini as high as a segment that spans almost the whole protein chain. We conclude that a specific network of non-local interactions, the closure of one or several loops, can play an important role in determining the protein folding pathway at its early phases.

Predicting reactivities of protein surface cysteines as part of a strategy for selective multiple labeling.

A variety of biophysical methods used to study proteins requires protein modification using conjugated molecular probes. Cysteine is the main residue that can be modified without the risk of altering other residues in the protein chain. It is possible to label several cysteines in a protein using highly selective labeling reactions, if the cysteines react at very different rates. The reactivity of a cysteine residue introduced into an exposed surface site depends on the fraction of cysteine in the deprotonated state. Here, it is shown that cysteine reactivity differences can be effectively predicted by an electrostatic model that yields site-specifically the fractions of cysteinate. The model accounts for electrostatic interactions between the cysteinyl anion and side chains, the local protein backbone, and water. The energies of interaction with side chains and the main chain are calculated by using the two different dielectric constants, 40 and 22, respectively. Twenty-six mutants of Escherichia coli adenylate kinase were produced, each containing a single cysteine at the protein surface, and the rates of the reaction with 5,5'-dithiobis(2-nitrobenzoic acid) (Ellman's reagent) were measured. Cysteine residues were chosen on the basis of locations that were expected to allow modification of the protein with minimal risk of perturbing its structure. The reaction rates spanned a range of 6 orders of magnitude. The correlation between predicted fractions of cysteinate and measured reaction rates was strong (R = 92%) and especially high (R = 97%) for cysteines at the helix termini. The approach developed here allows reasonably fast, automated screening of protein surfaces to identify sites that permit efficient preparations of double- or triple-labeled protein.

15N relaxation study of the cold shock protein CspB at various solvent viscosities.

For a detailed NMR study of the dynamics of the cold shock protein CspB from Bacillus subtilis, we determined (15)N transverse and longitudinal relaxation rates and heteronuclear nuclear Overhauser effects at different solvent viscosities. Up to a relative viscosity of 2, which is equivalent to 27% ethylene glycol (EG), the overall correlation time follows the linear Stokes-Einstein equation. At a relative viscosity of 6 (70% EG) the correlation time deviates from linearity by 30%, indicating that CspB tumbles at a higher rate as expected from the solvent viscosity probably due to a preferential binding of water molecules at the protein surface. The corresponding hydrodynamic radii, determined by NMR diffusion experiments, show no variation with viscosity. The amplitudes of intramolecular motions on a sub-nanosecond time scale revealed by an extended Lipari-Szabo analysis were mainly independent of the solvent viscosity. The lower limit of the NMR 'observation window' for the internal correlation time shifts above 0.5 ns at 70% EG, which is directly reflected in the experimentally derived internal correlation times. Chemical exchange contributions to the transverse relaxation rates derived from the Lipari-Szabo approach coincide with the experimentally determined values from the transverse (1)H-(15)N dipolar/(15)N chemical shift anisotropy relaxation interference. These contributions originate from fast protein folding reactions on a millisecond timescale, which get retarded at increased solvent viscosities.

Water contributes actively to the rapid crossing of a protein unfolding barrier.

The cold-shock protein CspB folds rapidly in a N <= => U two-state reaction via a transition state that is about 90% native in its interactions with denaturants and water. This suggested that the energy barrier to unfolding is overcome by processes occurring in the protein itself, rather than in the solvent. Nevertheless, CspB unfolding depends on the solvent viscosity. We determined the activation volumes of unfolding and refolding by pressure-jump and high-pressure stopped-flow techniques in the presence of various denaturants. The results obtained by these methods agree well. The activation volume of unfolding is positive (Delta V(++)(NU)=16(+/-4) ml/mol) and virtually independent of the nature and the concentration of the denaturant. We suggest that in the transition state the protein is expanded and water molecules start to invade the hydrophobic core. They have, however, not yet established favorable interactions to compensate for the loss of intra-protein interactions. The activation volume of refolding is positive as well (Delta V(++)(NU)=53(+/-6) ml/mol) and, above 3 M urea, independent of the concentration of the denaturant. At low concentrations of urea or guanidinium thiocyanate, Delta V(++)(UN) decreases significantly, suggesting that compact unfolded forms become populated under these conditions.