Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer

Diffusion-controlled electron transfer processes and power-law statistics of fluorescence intermittency of nanoparticles

A mechanism involving diffusion-controlled electron transfer processes in Debye and non-Debye dielectric media is proposed to elucidate the power-law distribution for the lifetime of a blinking quantum dot. This model leads to two complementary regimes of power law with a sum of the exponents equal to 2, and to a specific value for the exponent in terms of a distribution of the diffusion correlation times. It also links the exponential bending tail with energetic and kinetic parameters.

Multipoint correlation functions for continuous-time random walk models of anomalous diffusion

Recursive relations are developed for computing the multipoint correlation functions of a particle undergoing a biased continuous-time random walk (CTRW) in an external potential. Two- and three-point correlation functions are calculated for waiting-time distributions with an anomalous power-law profile t(-alpha-1), 0 < alpha < 1, on intermediate time scales with a crossover to an exponential long time decay. Comparison of the CTRW with the Brownian harmonic oscillator model (Gaussian process) illustrates how higher-order correlation functions may be used to distinguish between dynamical models that have the same two-point correlation function.

Closed-form solutions for continuous time random walks on finite chains

Continuous time random walks (CTRWs) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function (propagator) and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions are also the Laplace space solutions of the generalized master equation. Moreover, based on our counting technique, we introduce the adaptor function for expressing higher order propagators (joint PDFs of time-position variables) for CTRWs in terms of Green's functions. Using the derived formula, an escape problem from a biased chain is considered.

On the relationships between kinetic schemes and two-state single molecule trajectories

Trajectories of a signal that fluctuates between two states which originate from single molecule activities have become ubiquitous. Common examples are trajectories of ionic flux through individual membrane channels and of photon counts collected from diffusion, activity, and conformational changes of biopolymers. By analyzing the trajectory, one wishes to deduce the underlying mechanism, which is usually described by a multisubstate kinetic scheme. In previous works [O. Flomenborn, J. Klafter, and A. Szabo, Biophys. J. 88, 3780 (2005); O. Flomenbom and J. Klafter, Acta Phys. Pol. B 36, 1527 (2005)], we divided kinetic schemes that generate two-state trajectories into two types: reducible schemes and irreducible schemes. A full characterization of the reducible ones was given. We showed that all the information in trajectories generated from reducible schemes is contained in the waiting time probability density functions (PDFs) of the two states. It follows that reducible schemes with the same waiting time PDFs are not distinguishable; namely, such schemes lead to identical two-state trajectories in the statistical sense. In this work, we further characterize the topologies of kinetic schemes, now of irreducible schemes, and further study two-state trajectories from the two types of scheme. We suggest various methods for extracting information about the underlying kinetic scheme from the trajectory (e.g., calculate the binned successive waiting times PDFs and analyze the ordered waiting time trajectories), and point out the advantages and disadvantages of each. We show that the binned successive waiting times PDFs are not only more robust than other functions when analyzing finite trajectories, but contain, in most cases, more information about the underlying kinetic scheme than other functions in the limit of infinitely long trajectories. For some cases, however, analyzing the ordered waiting times trajectory may supply unique information about the underlying kinetic scheme.

Energy dissipation in multichromophoric single dendrimers

Single-molecule spectroscopy of well-chosen dendritic multichromophoric systems allows investigation of fundamental photophysical processes such as energy or electron transfer in much greater detail than the respective ensemble measurements. In dendrimers with multiple chromophores, energy hopping and transfer to the chromophore with the energetically lowest S(1) state was observed. If more than one chromophore is in an excited state in one molecule, annihilation, either singlet-triplet or singlet-singlet, can occur. In the latter case, a higher singlet state is populated opening new deactivation pathways. In the presence of an electron donor, reversible electron transfer could be observed, and the rate constants of forward and backward electron transfer were established. The value of these rate constants fluctuates time-correlated with the rotational motion of the dendrimer arms and the mobility of the embedding matrix.

Quasielastic neutron scattering and relaxation processes in proteins: analytical and simulation-based models

The present article gives an overview of analytical and simulation approaches to describe the relaxation dynamics of proteins. Particularly emphasised are recent developments of theoretical models, such as fractional Brownian dynamics. The latter connects dynamical events seen on the pico- to nanosecond time scale, accessible to quasielastic neutron scattering, and functional dynamics of proteins on much longer time scales.

What can one learn from two-state single-molecule trajectories?

A time trajectory of an observable that fluctuates between two values (say, on and off), stemming from some unknown multisubstate kinetic scheme, is the output of many single-molecule experiments. Here we show that when all successive waiting times along the trajectory are uncorrelated the on and the off waiting time probability density functions contain all the information. By relating the lack of correlation in the trajectory to the topology of kinetic schemes, we can immediately specify those kinetic schemes that are equally consistent with experiment, and cannot be differentiated by any sophisticated analyses of the trajectory. Correlated trajectories, however, contain additional information about the underlying kinetic scheme, and we consider the strategy that one should use to extract it.

COREX/BEST server: a web browser-based program that calculates regional stability variations within protein structures

SUMMARY

Utilizing the user-supplied coordinates of a protein structure, the COREX/BEST Server generates a structural thermodynamic ensemble. This conformational ensemble can then be used to calculate the regional variations in stability of a protein structure, and the stabilities are presented in units of energy (kcal/mol). The regional stabilities, which are calculated at the resolution of individual residues, can be mapped onto the protein structure for visual representation and downloaded from the site in the form of tab delimited text. The site provides an easy to follow summary of the theoretical and algorithmic approaches and provides links to references for more detailed descriptions.

AVAILABILITY

The COREX/BEST Server may be accessed through a typical web browser by visiting http://best.utmb.edu/BEST/.

Ionization potentials of fluoroindoles and the origin of nonexponential tryptophan fluorescence decay in proteins

This work reports an explanation for the unusual monoexponential fluorescence decay of 5-fluorotryptophan (5FTrp) in single-Trp mutant proteins [Broos, J.; Maddalena, F.; Hesp, B. H. J. Am. Chem. Soc. 2004, 126, 22-23] and substantially clarifies the origin of the ubiquitous nonexponential fluorescence decay of tryptophan in proteins. Our results strongly suggest that the extent of nonexponential fluorescence decay is governed primarily by the efficiency of electron transfer (ET) quenching by a nearby amide group in the peptide bond. Fluoro substitution increases the ionization potential (IP) of indole, thereby suppressing the ET rate, leading to a longer average lifetime and therefore a more homogeneous decay. We report experimental IPs for a number of substituted indoles including 5-fluoroindole, 5-fluoro-3-methylindole, and 6-fluoroindole, along with accurate ab initio calculations of the IPs for these and 20 related molecules. The results predict the IP of 5-fluorotryptophan to be 0.19 eV higher than that of tryptophan. 5-Fluoro substitution does not measurably alter the excitation-induced change in permanent dipole moment nor does it change the fluorescent state from 1La to 1Lb. In combination with electronic structure information this argues that the increased IP and the decreased excitation energy of the 1La state, together 0.3 eV, are solely responsible for the strong reduction of electron transfer quenching. 6-Fluoro substitution is predicted to increase the IP by a mere 0.09 eV. In agreement with our conclusions, the fluorescence decay curves of 6-fluorotryptophan-containing proteins are well fit using only two decay times compared to three required for Trp.

Observation of a power-law memory kernel for fluctuations within a single protein molecule

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t(-0.51 +/- 0.07) in a broad range of time scales (10(-3)-10 s). Such a long-time memory effect could have implications for protein functions.

Branching Out of Single‐Molecule Fluorescence Spectroscopy: Challenges for Chemistry and Influence on Biology

In the last decade emerging single-molecule fluorescence-spectroscopy tools have been developed and adapted to analyze individual molecules under various conditions. Single-molecule-sensitive optical techniques are now well established and help to increase our understanding of complex problems in different disciplines ranging from materials science to cell biology. Previous dreams, such as the monitoring of the motility and structural changes of single motor proteins in living cells or the detection of single-copy genes and the determination of their distance from polymerase molecules in transcription factories in the nucleus of a living cell, no longer constitute unsolvable problems. In this Review we demonstrate that single-molecule fluorescence spectroscopy has become an independent discipline capable of solving problems in molecular biology. We outline the challenges and future prospects for optical single-molecule techniques which can be used in combination with smart labeling strategies to yield quantitative three-dimensional information about the dynamic organization of living cells.

Electron Transfer at the Single-Molecule Level in a Triphenylamine-Perylene Imide Molecule

Photoinduced electron transfer (ET) processes in a donor-acceptor system based on triphenylamine and perylene imide have been studied at the single-molecule (SM) and ensemble levels. The system exists as two isomers, one of which undergoes forward and reverse ET in toluene with decay constants of 3.0 and 2.2x10(9) s(-1), respectively, resulting in the dual emission of quenched and delayed fluorescence while the other isomer remains ET-inactive. The fluorescence of both isomers is heavily quenched in the more polar solvent, diethyl ether, by ET. A broad range of ET dynamics is seen at the SM level in polystryene with the two isomers nonresolvable indicating that the local nanoenvironment of the SMs varies considerably throughout the polymer matrix. Both the electronic coupling and the driving force for ET are shown to influence the ET dynamics. Many fluorescence trajectories of SMs show long periods (tens of milliseconds to seconds) where the count rate is attenuated either partly (a "dim" state) or to the background level (an "off-time"). During these periods, the reduction or interruption of emission is attributed to cycles of rapid charge separation followed by charge recombination to the ground state reducing the fluorescence quantum yield of the SM.

Visualizing and manipulating individual protein molecules

Single-molecule imaging and manipulation techniques have evolved in the past decade from mere jaw-dropping attractions to essential laboratory tools. By applying single-molecule methods important insights otherwise unavailable have been obtained on various biomolecular systems. Constantly improving single-molecule imaging techniques keep expanding the scale of the explorable spatial detail, thereby providing possible solutions to getting around the debilitating diffraction limit present in physiological-condition structural investigations. In some areas, such as motor protein studies, single-molecule methods have become part of the routine and essential research toolkit. Entire research fields, such as single-molecule force spectroscopy, have been born. In the present review single-molecule visualization and manipulation methods are reviewed with a focus on proteins. Relevant signals and prominent applications are discussed along with experimental examples and recent important results. Finally, the perspectives of the single-molecule field are explored.

Fluorophore−Quencher Distance Correlation Functions from Single-Molecule Photon Arrival Trajectories†

We generalize and simplify the method of Yang and Xie (J. Chem. Phys. 2002, 117, 10965) to obtain distance correlation functions from photon arrival trajectories of single fluorophores whose lifetime, [k(r)](-1), depends on the distance to a quencher. It is assumed that this distance does not change during the fluorescence lifetime. The experimental trajectory is first transformed by replacing the delay time (i.e., the interval between the photon arrival and the nearest laser pulse) by a certain function of this delay time. This function is the inverse Laplace transform of r(k), which is the solution of k(r) = 1. The correlation function of the transformed data then directly gives the distance correlation function. Illustrative examples include Förster energy transfer and quenching due to electron transfer.

Defining the role of active-site loop fluctuations in dihydrofolate reductase catalysis

Dynamic processes are implicit in the catalytic function of all enzymes. To obtain insights into the relationship between the dynamics and thermodynamics of protein fluctuations and catalysis, we have measured millisecond time scale motions in the enzyme dihydrofolate reductase using NMR relaxation methods. Studies of a ternary complex formed from the substrate analog folate and oxidized NADP+ cofactor revealed conformational exchange between a ground state, in which the active site loops adopt a closed conformation, and a weakly populated (4.2% at 30 degrees C) excited state with the loops in the occluded conformation. Fluctuations between these states, which involve motions of the nicotinamide ring of the cofactor into and out of the active site, occur on a time scale that is directly relevant to the structural transitions involved in progression through the catalytic cycle.

Imaging of Tautomerism in a Single Molecule

Fluorescence imaging is used to visualize directly the transfer of two inner hydrogen atoms in single porphycene molecules. This reaction leads to a chemically equivalent but differently oriented structure and hence results in a rotation of the transition dipole moments. By probing single immobilized molecules with an azimuthally polarized laser beam in the focal spot of a confocal microscope we observe ring-like emission patterns, possible only for a chromophore with two nearly orthogonal transition dipole moments. Numerical simulations of the observed emission patterns yield a value of 72 degrees for the angle between the S0-S1 transition moments in the two tautomeric forms.

Downhill kinetics of biomolecular interface binding: globally connected scenario

We study the kinetics of the biomolecular binding process at the interface using energy landscape theory. The global kinetic connectivity case is considered for a downhill funneled energy landscape. By solving the kinetic master equation, the kinetic time for binding is obtained and shown to have a U-shape curve-dependence on the temperature. The kinetic minimum of the binding time monotonically decreases when the ratio of the underlying energy gap between native state and average non-native states versus the roughness or the fluctuations of the landscape increases. At intermediate temperatures, fluctuations measured by the higher moments of the binding time lead to non-Poissonian, non-exponential kinetics. At both high and very low temperatures, the kinetics is nearly Poissonian and exponential.

Local conformational fluctuations can modulate the coupling between proton binding and global structural transitions in proteins

Local conformational fluctuations in proteins can affect the coupling between ligand binding and global structural transitions. This finding was established by monitoring quantitatively how the population distribution in the ensemble of microstates of staphylococcal nuclease was affected by proton binding. Analysis of acid unfolding and proton-binding data with an ensemble-based model suggests that local fluctuations: (i) can be effective modulators of ligand-binding affinities, (ii) are important determinants of the cooperativity of ligand-driven global structural transitions, and (iii) are well represented thermodynamically as local unfolding processes. These studies illustrate how an ensemble-based description of proteins can be used to describe quantitatively the interdependence of local conformational fluctuations, ligand-binding processes, and global structural transitions. This level of understanding of the relationship between conformation, energy, and dynamics is required for a detailed mechanistic understanding of allostery, cooperativity, and other complex functional and regulatory properties of macromolecules.

Single-molecule spectroscopy selectively probes donor and acceptor chromophores in the phycobiliprotein allophycocyanin

We report on single-molecule fluorescence measurements performed on the phycobiliprotein allophycocyanin (APC). Our data support the presence of a unidirectional Förster-type energy transfer process involving spectrally different chromophores, alpha84 (donor) and beta84 (acceptor), as well as of energy hopping amongst beta84 chromophores. Single-molecule fluorescence spectra recorded from individual immobilized APC proteins indicate the presence of a red-emitting chromophore with emission peaking at 660 nm, which we connect with beta84, and a species with the emission peak blue shifted at 630 nm, which we attribute to alpha84. Polarization data from single APC trimers point to the presence of three consecutive red emitters, suggesting energy hopping amongst beta84 chromophores. Based on the single-molecule fluorescence spectra and assuming that emission at the ensemble level in solution comes mainly from the acceptor chromophore, we were able to resolve the individual absorption and emission spectra of the alpha84 and beta84 chromophores in APC.

Short-range spectroscopic ruler based on a single-molecule optical switch

We demonstrate a novel all-optical switch consisting of two molecules: a primary fluorophore (Cy5) that can be switched between a fluorescent and a dark state by light of different wavelengths, and a secondary chromophore (Cy3) that facilitates switching. The interaction between the two molecules exhibits a distance dependence much steeper than that of conventional Fo rster resonance energy transfer. This enables the switch to act as a ruler with the capability to probe distances difficult to access by other spectroscopic methods, thus presenting a new tool for the study of biomolecules at the single-molecule level.

Structural flexibility of small GTPases. Can it explain their functional versatility?

Multiple interactions with many different partners are responsible for the amazing functional versatility of proteins, especially those participating in cellular regulation. The structural properties that could facilitate multiple interactions are examined for small GTPases. The role of cellular constraints, compartmentation and scaffolds on protein-protein interactions is considered.

Single-molecule enzymology of chymotrypsin using water-in-oil emulsion

Single-molecule studies allow the study of subtle activity differences due to local folding in proteins, but are time consuming and difficult because only a few molecules are observed in one experiment. We developed an assay where we can simultaneously measure the activity of hundreds of individual molecules. The assay utilizes a synthetic chymotrypsin substrate that is nonfluorescent before cleavage by chymotrypsin, but is intensely fluorescent afterward. We encapsulated the enzyme and substrate in micron-sized droplets of water surrounded by silicone oil where each microdroplet contains <1 enzyme on average. A microscope and charge-coupled device camera are used to measure the fluorescence intensity of the same individual droplet over time. Based on these measurements, we conclude that enzymatic reactions could occur within this emulsion system, the statistical average activity of individual chymotrypsin molecules is similar to that measured in bulk, and the activity of individual chymotrypsin is heterogeneous.

Agonist-mediated Conformational Changes in Acetylcholine-binding Protein Revealed by Simulation and Intrinsic Tryptophan Fluorescence

We delineated acetylcholine (ACh)-dependent conformational changes in a prototype of the nicotinic receptor ligand binding domain by molecular dynamics simulation and changes in intrinsic tryptophan (Trp) fluorescence. Prolonged molecular dynamics simulation of ACh-binding protein showed that binding of ACh establishes close register of Trps from adjacent subunits, Trp(143) and Trp(53), and draws the peripheral C-loop inward to occlude the entrance to the binding cavity. Close register of Trp(143) and Trp(53) was demonstrated by ACh-mediated quenching of intrinsic Trp fluorescence, elimination of quenching by mutation of one or both Trps to Phe, and decreased lifetime of Trp fluorescence by bound ACh. Occlusion of the binding cavity by the C-loop was demonstrated by restricted access of an extrinsic quencher of binding site Trp fluorescence by ACh. The collective findings showed that ACh initially establishes close register of conserved Trps from adjacent subunits and then draws the C-loop inward to occlude the entrance to the binding cavity.

Stretched exponential decay and correlations in the catalytic activity of fluctuating single lipase molecules

Single-molecule techniques offer a unique tool for studying the dynamical behavior of individual molecules and provide the possibility to construct distributions from individual events rather than from a signal stemming from an ensemble of molecules. In biological systems, known for their complexity, these techniques make it possible to gain insights into the detailed spectrum of molecular conformational changes and activities. Here, we report on the direct observation of a single lipase-catalyzed reaction for extended periods of time (hours), by using confocal fluorescence microscopy. When adding a profluorescent substrate, the monitored enzymatic activity appears as a trajectory of "on-state" and "off-state" events. The waiting time probability density function of the off state and the state-correlation function fit stretched exponentials, independent of the substrate concentration in a certain range. The data analysis unravels oscillations in the logarithmic derivative of the off-state waiting time probability density function and correlations between off-state events. These findings imply that the fluctuating enzyme model, which involves a spectrum of enzymatic conformations that interconvert on the time scale of the catalytic activity, best describes the observed enzymatic activity. Based on this model, values for the coupling and reaction rates are extracted.

Electron Transfer Reaction in a Single Protein Molecule Observed by Total Internal Reflection Fluorescence Microscopy

To observe an electron transfer (ET) process in a single protein molecule, we constructed a model system, Alexa-HCytb5, in which cytochrome b5 (Cytb5) is modified with a fluorescent probe, Alexa Fluor 647 dye. In this model system, intramolecular transfer of an electron from the Alexa dye to heme in Cytb5 is supposed to oxidize the probe and quench its fluorescence, and the ET reaction at the single-molecule level can be monitored as the intermittent change in the fluorescence intensity. Alexa-HCytb5 was fixed on the glass surface, and illumination of laser light by the total internal reflection resulted in blinking of the fluorescence from the single Alexa-HCytb5 molecule in the time scale of several hundred milliseconds. Each Alexa-HCytb5 molecule is characterized by its own rate constant of the blinking, corresponding to the ET rate constant at the single-molecule level, and its variation ranges between 1 and 10 s(-1). The current system thus enables us to visualize the ET reaction in the single protein molecule, and the protein ET reaction was found to be explained by the distribution of the rate constants. On the basis of the Marcus theory, we suggest that the origin of this rate distribution is the distance change associated with the structural fluctuation in the protein molecule.

Information bounds and optimal analysis of dynamic single molecule measurements

Time-resolved single molecule fluorescence measurements may be used to probe the conformational dynamics of biological macromolecules. The best time resolution in such techniques will only be achieved by measuring the arrival times of individual photons at the detector. A general approach to the estimation of molecular parameters based on individual photon arrival times is presented. The amount of information present in a data set is quantified by the Fisher information, thereby providing a guide to deriving the basic equations relating measurement uncertainties and time resolution. Based on these information-theoretical considerations, a data analysis algorithm is presented that details the optimal analysis of single-molecule data. This method natively accounts and corrects for background photons and cross talk, and can scale to an arbitrary number of channels. By construction, and with corroboration from computer simulations, we show that this algorithm reaches the theoretical limit, extracting the maximal information out of the data. The bias inherent in the algorithm is considered and its implications for experimental design are discussed. The ideas underlying this approach are general and are expected to be applicable to any information-limited measurement.

Theory of torsional non-Condon electron transfer: A generalized spin-boson Hamiltonian and its nonadiabatic limit solution

The paper develops a theory of electron transfer with torsionally induced non-Condon (NC) effects. The starting point of the theory is a generalized spin-boson Hamiltonian, where an additional torsional oscillator bilinearly coupled to other bath modes causes a sinusoidal NC modulation. We derive closed form time dependent nonadiabatic rate expressions for both sudden and relaxed initial conditions, which are applicable for general spectral densities and energetic condition. Under the assumption that the torsional motion is not correlated with the polaronic shift of the bath, simple stationary limit rate expression is obtained. Model calculations of this rate expression illustrate the effects of torsional quantization and gating on the driving force and temperature dependences of the electron transfer rate. The classical limit of the rate expression consists of three Marcus-type terms, and is shown to agree very well with the exact numerical result.

Mechanical Unfolding Intermediates Observed by Single-molecule Force Spectroscopy in a Fibronectin Type III Module

Domain 10 of type III fibronectin (10FNIII) is known to play a pivotal role in the mechanical interactions between cell surface integrins and the extracellular matrix. Recent molecular dynamics simulations have predicted that 10FNIII, when exposed to a stretching force, unfolds along two pathways, each with a distinct, mechanically stable intermediate. Here, we use single-molecule force spectroscopy combined with protein engineering to test these predictions by probing the mechanical unfolding pathway of 10FNIII. Stretching single polyproteins containing the 10FNIII module resulted in sawtooth patterns where 10FNIII was seen unfolding in two consecutive steps. The native state unfolded at 100(+/-20) pN, elongating (10)FNIII by 12(+/-2) nm and reaching a clearly marked intermediate that unfolded at 50(+/-20) pN. Unfolding of the intermediate completed the elongation of the molecule by extending another 19(+/-2) nm. Site-directed mutagenesis of residues in the A and B beta-strands (E9P and L19P) resulted in sawtooth patterns with all-or-none unfolding events that elongated the molecule by 19(+/-2) nm. In contrast, mutating residues in the G beta-strand gave results that were dependent on amino acid position. The mutation I88P in the middle of the G beta-strand resulted in native like unfolding sawtooth patterns showing an intact intermediate state. The mutation Y92P, which is near the end of G beta-strand, produced sawtooth patterns with all-or-none unfolding events that lengthened the molecule by 17(+/-2) nm. These results are consistent with the view that 10FNIII can unfold in two different ways. Along one pathway, the detachment of the A and B beta-strands from the body of the folded module constitute the first unfolding event, followed by the unfolding of the remaining beta-sandwich structure. Along the second pathway, the detachment of the G beta-strands is involved in the first unfolding event. These results are in excellent agreement with the sequence of events predicted by molecular dynamics simulations of the 10FNIII module.

Using Single-Molecule Fluorescence Spectroscopy to Study Electron Transfer

Techniques in single-molecule fluorescence spectroscopy now allow sophisticated studies of photophysical processes in single molecules. As interest grows in the possibilities of molecular electronics, researchers have begun to turn these techniques to the study of electron transfer. Electron-transfer reactions have now been detected and measured at the single-molecule level in a variety of systems and on a variety of timescales by adapting techniques from previous single-molecule fluorescence studies.

Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule

By introducing fractional Gaussian noise into the generalized Langevin equation, the subdiffusion of a particle can be described as a stationary Gaussian process with analytical tractability. This model is capable of explaining the equilibrium fluctuation of the distance between an electron transfer donor and acceptor pair within a protein that spans a broad range of time scales, and is in excellent agreement with a single-molecule experiment.

Fluorescence studies of single biomolecules

Single-molecule fluorescence has the capability to detect properties buried in ensemble measurements and, hence, provides new insights about biological processes. Ratiometric methods are normally used to reduce the effects of excitation beam inhomogeneity. Fluorescence resonance energy transfer is widely used but there are problems in inserting the fluorophores in the correct position on the biomolecule, particularly if the structure is not known. We have recently developed two-colour coincidence single-molecule fluorescence that addresses this problem. This method can be used to determine quantitatively the multimerization states of biomolecules, in solution without separation. The future prospects of single-molecule fluorescence as applied to biological molecules are discussed.

Dynamics of ATP-binding cassette contribute to allosteric control, nucleotide binding and energy transduction in ABC transporters

ATP-binding cassette (ABC) transporters move solutes across membranes and are associated with important diseases, including cystic fibrosis and multi-drug resistance. These molecular machines are energized by their charateristic ABC modules, molecular engines fuelled by ATP hydrolysis. A solution NMR study of a model ABC, Methanococcus jannaschii protein MJ1267, reveals that ADP-Mg binding alters the flexibilities of key ABC motifs and induces allosteric changes in conformational dynamics in the LivG insert, over 30A away from the ATPase active site. (15)N spin relaxation data support a "selected-fit" model for nucleotide binding. Transitions between rigidity and flexibility in key motifs during the ATP hydrolysis cycle may be crucial to mechanochemical energy transduction in ABC transporters. The restriction of correlated protein motions is likely a central mechanism for allosteric communications. Comparison between dynamics data from NMR and X-ray crystallography reveals their overall consistency and complementarity.

Single molecule kinetics. II. Numerical Bayesian approach

As discussed in the companion paper [J. B. Witkoskie and J. S. Cao, J. Chem. Phys. 121, 6361 (2004), preceding paper], quantitative extraction of information from single molecule experiments by several proposed indicators is difficult since the experiments only observe certain characteristics of the system, even though the indicators can contain all available information. This paper shows how one can circumvent the shortcomings of these indicators by combining information extracted from indicators with a numerical Bayesian statistical approach. The Bayesian approach determines the relative probability of various models reproducing the entire sequence of the single molecules trajectory, instead of binning and averaging over the data, which removes much of this information.

Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments (for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.

Single molecule kinetics. I. Theoretical analysis of indicators

Single molecule experiments reveal intriguing phenomenon in chemical and biological systems. Several indicators of complex dynamics, including "intensity" correlations, "event" correlations, and characteristic functions have been proposed, but extraction of information from these indicators can be difficult since these indicators only observe certain characteristics of the system. Generally, for systems that follow Poisson kinetics, all of these indicators contain similar information about the relaxation times of the system and the connections between different relaxation times, but the information is convoluted in different ways so the strength of various indicators is system specific. The paper discusses the theoretical implications and information content of various data analysis methods for single molecule experiments and demonstrates the relationships between indicators. Under certain conditions, common indicators contain all available information about systems with Poisson kinetics between degenerate states, but extraction of this information is generally not numerically feasible. The paper also discusses practical issues associated with these analyses, which motivates a numerical study based on Bayes' formula in the companion paper [J. Witkoskie and J. S. Cao, J. Chem. Phys. 121, 6373 (2004), following paper].

Probing conformational dynamics in single donor-acceptor synthetic molecules by means of photoinduced reversible electron transfer

We use single-molecule fluorescence lifetimes to probe dynamics of photoinduced reversible electron transfer occurring between triphenylamine (donor) and perylenediimide (acceptor) in single molecules of a polyphenylenic rigid dendrimer embedded in polystyrene. Here, reversible electron transfer in individual donor-acceptor molecules results in delayed fluorescence that is emitted with a high photon count rate. By monitoring fluorescence decay times on a photon-by-photon basis, we find fluctuations in both forward and reverse electron transfer spanning a broad time range, from milliseconds to seconds. Fluctuations are induced by conformational changes in the dendrimer structure as well by polystyrene chain reorientation. The conformational changes are related to changes in the dihedral angle of adjacent phenyl rings located in the dendritic branch near the donor transferring the charge, a torsional motion that results in millisecond fluctuations in the "through-bond" donor-acceptor electronic coupling. Polymer chain reorientation leads to changes in the local polarity experienced by the donors and to changes in the solvation of the charge-separated state. As a result, switching between different donor moieties within the same single molecule becomes possible and induces fluctuations in decay time on a time scale of seconds.