Resonance Transfer Of Excitation Energy Research Articles

Förster Resonance Energy Transfer between Fluorescent Organic Semiconductors: Poly(9,9-dioctylfluorene-alt-benzothiadiazole) and 6,13-Bis(triisopropylsilylethynyl)pentacene

In the present study, an investigation of the electronic excitation energy transfer between two p-type fluorescent semiconductors, F8BT [poly(9,9-dioctylfluorene-alcohol-benzothiadiazole] and TIPS-P [6,13-bis(triisopropylsilylethynyl)pentacene], has been carried out in a chloroform solution using steady-state and time-domain fluorescence techniques. The spectral overlap integral between donor (F8BT) emission and acceptor (TIPS-P) absorption is 2.04 × 1015 nm4/(M cm), and the corresponding critical transfer distance is 53.12 Å. In donor decay dynamics, at the lower acceptor concentrations, the observed results deviate from the Förster theory due to the combined effect of diffusion and energy migration. However, it does not exhibit energy migration and distribution for higher acceptor concentrations, and the system follows the Förster model of resonance excitation energy transfer (FRET). The higher value of the donor-acceptor interaction strength than self-interaction (donor-donor interaction) appears to be responsible for this behavior. Further, in acceptor decay, the appearance of the rise time and its decrease with the acceptor concentration confirms FRET from F8BT to TIPS-P.

FLUORESCENT PROPERTIES OF DOXYCYCLINE IN PRESENCE OF SILVER NANOCLUSTERS

The paper shows that in the presence of silver nanoparticles the efficiency of intramolecular energy transfer in the complex of europium with doxycycline increases. It is proved that sensitivity of determination increases and limit of detection of doxycycline decreases by the method of sensitized fluorescence. The justification of the observed effects is given. The amplification of the signal of sensitized fluorescence in the presence of silver nanoparticles (energy donor) is the result of resonant transfer of excitation energy between the nanoparticle and the antibiotic ion, which is implemented under conditions of overlapping of the local surface plasmon resonance spectrum and excitation of the doxycycline ligand located near the surface of the nanoparticle. As a result of exposure to the antibiotic external radiation source and the local field of the surface plasmon increases the efficiency of tetracycline excitation, which contributes to the effectiveness of intramolecular energy transfer in europium chelate with doxycycline, doubling the intensity and lifetime. Modification of the surface of silver nanoparticles by europium ions allows to reduce the distance between the surface of a nanoparticle and an antibiotic, to increase the intensity of the signal of sensitized fluorescence by more than 100 times. The role of the stabilizer of a non-chromophore-containing ligand, − citrateion, in the formation of the analytical signal lies in its participation in the formation of a multi-ligand Eu3+ complex on the surface of a nanoobject, which reduces the distance between the donor and the acceptor, as well as the additional removal of water molecules from the immediate environment of the complexing agent ion, suppressing the process of excitation energy dissipation. On the basis of the conducted researches the fluorimetric technique of definition of doxycycline in medicines is offered. It differs in a low limit of detection (6.0·10-9 M) and a wide range of the defined concentrations from 1.0·10-8 to 1.0·10-5 M.

Cation Specific Effects on the Domain-Domain Interaction of Heterogeneous Dimeric Protein Revealed by FRET Analysis.

Specific monovalent cation effects on the domain-domain interaction of heterogeneous dimeric protein were investigated using green fluorescent protein (GFP)-glutathione-s-transferase (GST) fusion protein as a model protein. Conjugating N-terminal of GST domain with a fluorescence probe Cyanine3, complementary increase and decrease of fluorescence intensities of Cyanine3 and GFP were recognized on the exclusive excitation of GFP and further the fluorescence decay of GFP was remarkably accelerated to show that an excellent Förster type of resonance excitation energy transfer (FRET) pair was constructed between GFP- and GST-domain. The spectral overlap integral and critical distance of the FRET pair were estimated to be 5.96×1013 M-1cm3 and 62.5 Å, respectively. The FRET rate and efficiency evaluated by fluorescence lifetime of the energy donor, GFP, were influenced by the monovalent cations included in the buffer solution to suggest that the domain-domain interactions of GFP-GST fusion protein would be susceptible to cation species and their concentrations. The order affecting the domain-domain interaction was estimated to be Li+>NH4+ >Na+>K+>Cs+, almost corresponding to the reverse Hofmeister series.

Mediation of resonance energy transfer by two polarisable particles.

The molecular quantum electrodynamics theory is employed to calculate the matrix element and Fermi golden rule rate for resonant transfer of electronic excitation energy between a donor and an acceptor in the vicinity of two neutral electric dipole polarizable particles, which play the role of bridging species. The emitter and absorber couple linearly to the electric displacement field via their electric dipole moments, while each mediator interacts quadratically with this field through its dynamic polarizability. This form of interaction Hamiltonian enables fourth-order perturbation theory to be used to compute the probability amplitude together with summation over 24 time-ordered diagrams representing a single virtual photon exchange between each pair of coupled particles. Expressions for the migration rate mediated by two inert molecules are obtained for an arbitrary arrangement of the four species that are in fixed mutual orientation or are freely tumbling. These formulae are valid for all interparticle separation distances outside the orbital overlap region. From the general result, rate equations applicable to an equidistant collinear configuration of the four bodies are evaluated. Near- and far-zone limiting forms of the transfer rate for the relay pathway are also calculated and exhibit inverse sixth and inverse square dependences on relative separation distances between pairs of particles, confirming the short-range (radiationless) and long-range (radiative) energy transfer mechanisms associated with two-body theory. The distance behavior of interference terms between two-, three-, and four-body terms is also examined, and the relative importance of each contribution to the total transfer rate is discussed.

Ligand-Induced Conformational Changes near the Active Site Regulating Enzyme Activity of Momorcharins from Seeds of Bitter Gourd.

It is reasonable to consider that Type I-ribosomal inactivation proteins (RIP) retain some specific affinity to harmful pathogens to complete the role as a bio-defense relating protein. In the present studies, it was shown that two Type I-RIPs, α- and β-momorcharins, maintained the abilities to bind with N-acetylglucosamine (NAG) to change the conformation around the active sites and to regulate their N-glycosidase activities. By the binding of NAG, the freedom of internal motion of Trp192 in α-momorcharin was increased 1.5 times near the active site and, on the other hand, the corresponding motion of Trp190 was limited 50% in β-momorcharin. The results in the fluorescence resonance excitation energy transfer experiments demonstrated that Trp-190 of β-momorcharin was kept away from Tyr-70 but Trp192 contrarily approached closer to the nearest neighboring Tyr residue consisting of the active center of α-momorcharin by the binding with NAG. These conformational changes near the active site close correlated with promotion and/or suppression of the N-glucosidase activities of β- and α-momorcharins.

Effect of an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions on excitation energy transfer.

A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton-phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton-phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.

Self-Activated Low-Dimensional Metal Halide Phosphors and Scintillators

We report theoretical studies of exciton excitation and emission in low-dimensional metal halides, (C4N2H14X)4SnX6 (X = Br, I), Cs4PbBr6, (Ph4P)2SbCl5 (Ph4P = tetraphenylphosphonium), (C9NH20)2SnBr4, and (C4N2H14)PbCl4. These are bulk crystalline materials, in which isolated metal halide clusters/wires are separated from each other by large inorganic or organic countercations, forming 0D/1D structures. For example, in (C9NH20)2SnBr4, the anionic (SnBr4)2- clusters are separated from each other by (C9NH20)+ molecular countercations. The metal halides shown above all have 0D structures except (C4N2H14)PbCl4, which has a 1D wire structure. High photoluminescence quantum efficiencies (PLQE) (close to 100% in some cases) have been reported for the 0D metal halides. We calculated exciton excitation and emission energies in these low-dimensional metal halides; the results are in excellent agreement with the experimental values. This enables us to study the luminescence mechanisms and suggest new compounds for synthesis. We show that exciton self-trapping in the metal-halide cluster/wire leads to localized excitons, which is important for efficient radiative recombination. The relatively low PLQE (6% - 18%) in 1D (C4N2H14)PbCl4 is likely due to the exciton diffusion along the wire and the subsequent nonradiative recombination at defects. The large organic countercations in hybrid organic-inorganic 0D halides plays the important role of decoupling metal halide clusters (which are luminescent centers), leading to highly immobile excitons and high PLQE. On the other hand, in all inorganic 0D Cs4PbBr6, the significant electronic coupling between PbBr6 clusters and the small Stokes shift should enable resonant transfer of excitation energy and the subsequent energy loss at defects, which explains the strong thermal quenching of luminescence in Cs4PbBr6. We further suggest that Cs4EuX6 (X = Br,I), which are analogs to Cs4PbBr6, should exhibit improved luminescent properties compared to Cs4PbBr6 due to stronger exciton localization at Eu2+ than at Pb2+. Indeed, recent synthesis and characterization of these compounds show high light yields under gamma-ray irradiation at room temperature. In particular, the light yield of Cs4EuBr6 (78,000 photons/MeV) is the highest among the self-activated scintillators.

Resonant electronic excitation energy transfer by exchange mechanism in the quantum dot system

A microscopic theory of nonradiative resonance energy transfer between spherical A3B5 semiconductor quantum dots by the exchange mechanism is suggested. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same A3B5 compound and are embedded in the matrix of another material that produces potential barriers for electrons and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found in the frame of the Kane model that provides the most adequate description of the real spectra of A3B5 semiconductors. The analytical treatment is carried out with using the density matrix method, which enabled us to perform an energy transfer analysis both in the weak-interaction approximation and in the strong-interaction approximation. The numerical calculations showed the saturation of the energy transfer rate at the distances between the donor and the acceptor approaching the contact one. The contributions of the exchange and direct Coulomb intractions can be of the same order at the small distances and can have the same value in the saturation range.

Facile Design of a Plasmonic Nanolaser

A spaser consists of a plasmonic noble-metal nanostructure that acts as nanocavity, when incorporated or surface-coupled two-level emitters constitute the nanoscale gain medium. Suited two-level emitters are, for instance, laser dyes. Optical pumping may provide efficient excitation energy transfer between the two-level emitters in the gain medium and the surface plasmons sustained in the nanocavity. Strong resonant coupling of the surface plasmon modes to the gain medium may establish an inherent feedback amplification mechanism which finally drives the spaser action. In this contribution, we demonstrate that spaser emission can be generated by amplifying longitudinal surface plasmon modes in gold nanorods by optically pumping surface-attached resonantly-coupled laser dyes. Therefore, we synthesized gold nanorods whose longitudinal surface plasmon resonance peak was adjusted between 680 and 700 nm. The gain medium was realized by electrostatically attaching the laser dye phthalocyanine tetrasulfonate via the positively-charged CTAB (cetyltrimethylammonium bromide) bilayer to the gold-nanorod surface. Phthalocyanine tetrasulfonate exhibits fluorescence at 700 nm. Fluorescence quenching experiments unambiguously gave indication of resonant excitation energy transfer. The fluorescence intensity ratio I F 0 / I F follows the Stern–Volmer relationship, and the Stern–Volmer coefficient was determined as KSV = 1.22 × 106 M−1. The spaser emission was observed in fs transient absorption spectra as an ultrafast decaying narrow emission peak around 716 nm.

Resonant electronic excitation energy transfer by Dexter mechanism in the quantum dot system

In present work the energy transfer between quantum dots by the exchange (Dexter) mechanism is analysed. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same compound A3B5 and embedded in the matrix of other material creating potential barriers for electron and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found using the Kane model that provides the most adequate description spectra of semiconductors A3B5. Numerical calculations show that the rate of the energy transfer by Dexter mechanism is comparable to the rate of the energy transfer by electrostatic mechanism at the distances approaching to the contact ones.

Resonant excitation energy transfer from carbon dots to different sized silver nanoparticles.

The influence of size on the efficiency of the nanometal surface energy transfer (NSET) process between excited donors and different sized metal nanoparticles (NPs) is poorly explored in the literature. Here we present a systematic study by correlating the size of silver nanoparticles (Ag NPs) with the efficiency of excitation energy transfer (EET) from carbon dots (CDs) to Ag NPs. Three different sized citrate-capped Ag NPs with a mean hydrodynamic diameter of 39.91 ± 1.03, 53.12 ± 0.31 and 61.84 ± 0.77 nm have been synthesized for the present study. The estimated zeta potential of the synthesized CD is -25.45 ± 1.23 mV while that for the smallest, medium and largest sized Ag NPs are -76.24 ± 3.92, -67.60 ± 4.40, and -58.01 ± 3.10 mV, respectively. The steady-state and time-resolved PL measurements reveal a significant PL quenching of CDs as a function of Ag NP size. A control experiment with Ag NPs having a LSPR at 398 nm shows a negligible amount of PL quenching of CDs as a consequence of inadequate spectral overlap. The origin behind this PL quenching of CDs has been rationalized on the basis of the increased nonradiative decay rate due to NSET from the CDs to the Ag NP surface. Various energy transfer related parameters have been estimated from the NSET theory and it has been observed that the NSET efficiency increases with the increase in the size of Ag NPs. This phenomenon has been explained by considering a larger spectral overlap and a shorter separation distance between the CDs and larger sized Ag NPs due to reduced electrostatic repulsion. Our present results reveal that the size of NPs plays an important role in the NSET process and this phenomenon can be easily utilized to tune the efficiency of energy transfer for various applications.

Sm3+ doped TiO2 as optical oxygen sensor material

The luminescence properties of Sm3+ in sol–gel-made nanostructural TiO2 were shown to depend on surrounding gas environment. Both the intensity and lifetime of the luminescence increased with increasing oxygen content varied between 0% and 100% in the O2/N2 mixture at normal pressure. The luminescence decay kinetics after pulsed excitation at 355nm followed the stretched exponential function with the value of stretching exponent equal to 0.4–0.5. The mechanism of oxygen sensitivity was interpreted as resonant excitation energy transfer from Sm3+ to the acceptor defects, the latter being switched on and off the resonance by electron exchange with surface-adsorbed oxygen. Oxygen vacancy related defects were proposed as most likely candidates of energy acceptors. The studied material can be used for luminescence lifetime based oxygen sensing.

Spectroscopic manifestations of hybrid association of CdS colloidal quantum dots with J-aggregates of a thiatrimethine cyanine dye

We have found spectroscopic manifestations of hybrid association in mixtures of CdS colloidal quantum dots with an average size of 2.5–4.2 nm with J-aggregates of pyridinium salt of the 3,3'-di-(γ- sulfopropyl)-9-ethyl-4,5,4',5'-dibenzo-thiacarbocyanine betaine dye that were prepared by the sol–gel method in gelatin. Observed changes of the spectral properties of J-aggregates of dye molecules due to their hybrid association with CdS quantum dots are ensured by steric transformations of dye molecules, which lead to the formation of luminescent trans-J-aggregates. The hybrid association is accompanied by the quenching of the recombination luminescence band of CdS quantum dots (540–640 nm) and by an increase in the luminescence intensity of J-aggregates of dye molecules (670–680 nm). This regularity becomes enhanced with an increase in the ratio of the number of dye molecules to the number of quantum dots [ndye]: [nQD] and in the degree of overlap between the luminescence spectrum of quantum dots and the absorption spectrum of J-aggregates, which indicates that there is a resonant nonradiative transfer of the electronic excitation energy from recombination luminescence centers in CdS quantum dots to trans-J-aggregates of dye molecules conjugated to them.

Virtual photon exchange, intermolecular interactions and optical response functions

According to molecular quantum electrodynamics, coupling between material particles occurs due to an exchange of one or more virtual photons. In this work, the relationship between polarisability and hyperpolarisability tensors of atoms and molecules that feature in linear and nonlinear optical processes, and their analytically continued form in the complex frequency domain that appear in formulae describing fundamental inter-particle interactions, is studied. Examples involving a single virtual photon exchange, which are linearly proportional to electric dipole moments at each centre, include the electrostatic energy and the resonant transfer of excitation energy. The Casimir–Polder dispersion potential, and its discriminatory counterpart applicable to coupled chiral molecules, are used to illustrate response properties depending on the exchange of two virtual photons. Meanwhile, the energy shift between two hyperpolarisable species, a higher order discriminatory contribution to the dispersion potential, is employed to represent forces arising from the three virtual photon exchange. It is shown that for energy shifts that are quadratic or bilinear or cubic in the transition dipole moment, it is necessary to account for all two- and three-photon optical processes, such as absorption, emission and linear and nonlinear scattering of light in order to arrive at the correct form of the molecular response tensor.

Infrared Fluorescent Protein iRFP as an Acceptor for Förster Resonance Energy Transfer

Bacteriophytochrome-based infrared fluorescent protein iRFP was tested as an acceptor for F6rster resonance energy transfer (FRET). Far-red GFP-like fluorescent proteins mKate2, eqFP650, and eqFP670 were used as donors; Bacterial expression vectors encoding donor and acceptor proteins fused by a 17-amino acid linker were.constructed. FRET for purified proteins in vitro was, estimated from increase of the donor emission after digestion of the linker. Among the three constructs tested, the most efficient FRET (approximately 30%) was detected for the eqFP650-iRFP pair.

Nanotubular J-aggregates and quantum dots coupled for efficient resonance excitation energy transfer.

Resonant coupling between distinct excitons in organic supramolecular assemblies and inorganic semiconductors is supposed to offer an approach to optoelectronic devices. Here, we report on colloidal nanohybrids consisting of self-assembled tubular J-aggregates decorated with semiconductor quantum dots (QDs) via electrostatic self-assembly. The role of QDs in the energy transfer process can be switched from a donor to an acceptor by tuning its size and thereby the excitonic transition energy while keeping the chemistry unaltered. QDs are located within a close distance (<4 nm) to the J-aggregate surface, without harming the tubular structures and optical properties of J-aggregates. The close proximity of J-aggregates and QDs allows the strong excitation energy transfer coupling, which is around 92% in the case of energy transfer from the QD donor to the J-aggregate acceptor and approximately 20% in the reverse case. This system provides a model of an organic-inorganic light-harvesting complex using methods of self-assembly in aqueous solution, and it highlights a route toward hierarchical synthesis of structurally well-defined supramolecular objects with advanced functionality.

Fast closure of long loops at the initiation of the folding transition of globular proteins studied by time-resolved FRET-based methods

Abstract The protein folding problem would be considered “solved” when it will be possible to “read genes”, i.e., to predict the native fold of proteins, their dynamics, and the mechanism of fast folding based solely on sequence data. The long-term goal should be the creation of an algorithm that would simulate the stepwise mechanism of folding, which constrains the conformational space and in which random search for stable interactions is possible. Here, we focus attention on the initial phases of the folding transition starting with the compact disordered collapsed ensemble, in search of the initial sub-domain structural biases that direct the otherwise stochastic dynamics of the backbone. Our studies are designed to test the “loop hypothesis”, which suggests that fast closure of long loop structures by non-local interactions between clusters of mainly non-polar residues is an essential conformational step at the initiation of the folding transition of globular proteins. We developed and applied experimental methods based on time-resolved resonance excitation energy transfer (trFRET) measurements combined with fast mixing methods and studied the initial phases of the folding of Escherichia coli adenylate kinase (AK). A series of AK mutants were prepared, in which the ends of selected backbone segments that form long closed loops or secondary structure elements were labeled by donors and acceptors of excitation energy. The end-to-end distance distributions of such segments were determined under equilibrium and during the fast folding transitions. These experiments show that three out of seven long loops that were labeled in the AK molecule are closed very early in the transition. The N terminal 26-residue loop (loop I) is closed in &lt;200 μs after the initiation of folding, while the β strand included in loop I is still disordered. The closure of the second 44-residue loop (loop II, which starts at the end of loop I) is also complete within &lt;300 μs. Four other loops as well as five secondary structures of the CORE domain of AK (an α helix and four β strands) are formed at a late step, at a rate of 0.5±0.3 s–1, the rate of the cooperative folding of the molecule. These experiments reveal a hierarchically ordered pathway of folding of the AK molecule, ranging from microseconds to seconds. The results reviewed here, obtained mainly from studying a small number of model proteins, support the counterintuitive mechanism whereby non-local interactions are effective in the initiation of the folding pathways. The experiments presented demonstrate the importance of mapping the rates of sub-domain structural transitions along the folding transition, in situ, in the context of the other sections of the chain, whether folded or disordered. These experiments also show the power of the time-resolved FRET measurements in achieving this goal. A large body of data obtained by theoretical and experimental studies that support, or can accommodate, the loop hypothesis is reviewed. We suggest that mapping multiple sub-domain structural transitions during the refolding transition of many proteins using the approach presented here will refine the conclusions and help reveal some common principles of the initiation of the folding. To achieve this goal, the trFRET measurements should be combined with mutagenesis experiments where the role of selected residue clusters will be tested by perturbation mutations. Nevertheless, the solution of the protein folding problem depends on the application of many additional approaches, both experimental and theoretical, while the approach presented here is only a small section of the big puzzle.

Spectral characteristics of nanoamorphous phosphors obtained by evaporation of Sr2Gd8(SiO4)6O2: Eu polycrystals

Amorphous nanophosphors have been obtained for the first time by pulsed electron beam evaporation of targets from bulk polycrystalline phosphors of the composition Sr2Gd8(SiO4)6O2: Eu with oxyapatite structure. The processes of crystallization of amorphous nanopowder were studied using differential scanning calorimetry and termogravimetry (40−1400°C). It was found that the Raman spectra of the samples are modified when the particles decrease from bulk to nanodimensional state. The spectral and luminescent characteristics of the phosphors in polycrystalline and nanoamorphous states have been examined. It was established that Eu3+ forms two types of optical centers. Unlike bulk phosphors, in the nanophosphors no Eu2+ ions are formed. The ratio of red to orange luminescence intensity for nanophosphors was found to increase as compared with bulk phosphors. This effect is due to disordering of nanoparticles. A resonant transfer of excitation energy from Gd3+ to Eu3+ ions was found in bulk and nanophosphors. Upon transition from polycrystalline to nanoamorphous state and laser excitation of phosphors, the luminescence intensity of Eu3+ ions increases approximately 10 times. This effect is explained in the framework of the configuration coordinates model.

Excitation of mercury atoms in nitrogen post-discharge

The work presents results obtained during spectroscopic observations of nitrogen DC flowing post-discharges at the total gas pressure of 1000 Pa and at the discharge current of 100 mA. Mercury traces were introduced into the system using auxiliary pure nitrogen flow enriched by mercury vapor. A very low mercury concentration of 3.7 ppb was introduced into the system before the active discharge. The strong quenching of nitrogen pink afterglow was observed but no mercury lines were recorded. Moreover, the vibrational distributions of nitrogen excited states were nearly unchanged. Based on these results, the new experimental set up was created. The introduction point of mercury vapor with higher concentration of 600 ppm was movable during the post discharge up to decay time of 40 ms. Besides three nitrogen spectral systems (first and second positive and first negative), NOβ and NOγ bands, the mercury line at 254 nm was recorded at these conditions. Its intensity was dependent on the mercury vapor introduction position as well as on the mercury concentration. No other mercury lines were observed. The creation of mercury 3P1 state that is the upper state of the observed mercury spectral line is possible by the resonance excitation energy transfer form vibrationally excited nitrogen ground state N2(X1Σ+g, v = 19). The observed results should form a background for the development of a new titration technique used for the highly vibrationally excited nitrogen ground state molecules determination.

Fast closure of N-terminal long loops but slow formation of β strands precedes the folding transition state of Escherichia coli adenylate kinase.

The nature of the earliest steps of the initiation of the folding pathway of globular proteins is still controversial. To elucidate the role of early closure of long loop structures in the folding transition, we studied the folding kinetics of subdomain structures in Escherichia coli adenylate kinase (AK) using Förster type resonance excitation energy transfer (FRET)-based methods. The overall folding rate of the AK molecule and of several segments that form native β strands is 0.5 ± 0.3 s(-1), in sharp contrast to the 1000-fold faster closure of three long loop structures in the CORE domain. A FRET-based "double kinetics" analysis revealed complex transient changes in the initially closed N-terminal loop structure that then opens and closes again at the end of the folding pathway. The study of subdomain folding in situ suggests a hierarchic ordered folding mechanism, in which early and rapid cross-linking by hydrophobic loop closure provides structural stabilization at the initiation of the folding pathway.