We use the statistics of photon emission from single molecules to probe ultrafast dynamics an unfolded protein via Förster resonance energy transfer. Global reconfiguration chain occurs on a time scale ≈50 ns and slows down concomitant with collapse under folding conditions. These diffusive provide missing link between phenomenological chemical kinetics commonly used in physical description terms quantitative free surfaces. The experiments demonstrate potential single-molecule methods...

To obtain quantitative information on the size and dynamics of unfolded proteins we combined single-molecule lifetime intensity FRET measurements with molecular simulations. We compared states 64-residue, alpha/beta protein L 66-residue, all-beta cold-shock CspTm. The average radius gyration (Rg) calculated from data freely diffusing molecules was identical for two at guanidinium chloride concentrations >3 M, FRET-derived Rg agreed well previously measured by equilibrium small-angle x-ray...

Polyproline has recently been used as a spacer between donor and acceptor chromophores to help establish the accuracy of distances determined from single-molecule Förster resonance energy transfer (FRET) measurements. This work showed that FRET efficiency in water is higher than expected for rigid was attributed flexibility polypeptide. Here, we investigate this issue further, using combination fluorescence intensity lifetime measurements, NMR, theory, molecular dynamics simulations...

Conformational dynamics of a single molecule can be studied using Forster resonance energy transfer (FRET) by recording sequence photons emitted donor and an acceptor dye attached to the molecule. We describe simple robust method estimate rates transitions between different conformational states FRET efficiencies associated with these states. For photon trajectory measured interphoton times, pattern colors is decoded maximizing appropriate likelihood function. This approach used analyze...

We present the theory for distribution of number donor and acceptor photons detected in a time bin corresponding energy-transfer efficiency obtained from single-molecule Förster resonance measurements. Photon counts both immobilized freely diffusing molecules are considered. Our starting point is joint system described by an arbitrary kinetic scheme. This simplified exploiting scale separation between fast fluorescent transitions slow processes which include conformational dynamics,...

Single-molecule spectroscopy can monitor transitions between two microscopic states when these are associated with the emission of photons. A general formalism is developed for obtaining statistics such from a model dynamics described by master or rate equations their continuum analog, multidimensional reaction-diffusion equations. The focus on distribution number during fixed observation time, times transitions, and corresponding correlation functions. It shown how quantities related to...

In single-molecule FRET experiments with pulsed lasers, not only the colors of photons but also fluorescence lifetimes can be monitored. Although these quantities appear to random, they are modulated by conformational dynamics. order extract information about such dynamics, we develop theory joint distribution efficiencies and determined from bins (or bursts) photons. Our starting point is a rigorous formal expression for numbers donor acceptor in bin that treats influence dynamics on all...

Under relatively mild conditions, we show how one can extract information about conformational dynamics from Förster resonance energy transfer (FRET) experiments on diffusing molecules without modeling diffusion. Starting a rigorous theory that does treat diffusion, first examine when the single-molecule FRET efficiency distribution be decomposed into measured of total number photons and an immobilized molecule in absence shot noise. If conformation not change during time spends laser spot,...

Recently developed statistical methods by Gopich and Szabo were used to extract folding unfolding rate coefficients from single-molecule Förster resonance energy transfer (FRET) data for proteins with kinetics too fast measure waiting time distributions. Two types of experiments two different analyses performed. In one experiment bursts photons collected donor acceptor fluorophores attached a 73-residue protein, α3D, freely diffusing through the illuminated volume confocal microscope system....

Single-molecule spectroscopy is widely used to study macromolecular dynamics. Although this technique provides unique information that cannot be obtained at the ensemble level, possibility of studying fast molecular dynamics limited by number photons detected per unit time (photon count rate), which proportional illumination intensity. However, simply increasing intensity often does not help because various photophysical and photochemical problems. In Perspective, we show how improve dynamic...

What is the dynamical and structural information contained in single-molecule fluorescence resonance energy transfer (FRET) experiments where donor acceptor photons emitted during a fixed time window T are counted? To answer this question, theory developed to obtain probability distribution of energy-transfer efficiency obtained from trajectories duration T. The an explicit function distance between fluorescent attached macromolecule; thus, can formally be converted distance. resulting or,...

Fluorescence intensity correlation functions contain information about photophysical and conformational dynamics. We propose implement a simple procedure to analyze such measured in the presence of resonance energy transfer. When there is separation time scales dynamics modeled as diffusion potential mean force along interdye distance, we obtain an analytic expression for time. This can be used find coefficient describing fluctuations given photon count rate equilibrium distribution.

A simple analytic theory is developed to describe FRET efficiency histograms constructed from a photon trajectory generated by molecule with multiple conformational states. The are approximated sum of Gaussians the parameters explicitly determined efficiencies states and rates transitions between theory, which has been tested against exact for two simulated data three four states, accurately describes how peaks in collapse as bin time or transition increase.

The simplest general theory of the kinetics reversible diffusion-influenced reactions that is exact both at short and long times for A+B⇌C A+B⇌C+D presented. formalism based on an approximate set reaction-diffusion equations pair distribution functions which incorporate influence chemical reaction by using effective rate constants are determined self-consistently. For small deviations from equilibrium contact reactivity, relaxation function given explicitly in Laplace domain terms...

We obtain an accurate long-time solution for the diffusive kinetics of excited geminate pair dissociating reversibly in solution, where excited-state lifetimes bound and unbound states may be nonequal. analyze asymptotic behavior, finding a transition between two types behaviors. In region A, decays as t−3/2 exp(−t/τ0′), τ0′ is lifetime state. AB, decay pure exponential. At critical value parameters occurs, we find t−1/2 exp(−t/τ0′) decay. These predictions are tested against exact numerical...

Significance Intrinsically disordered proteins often form pathological oligomers implicated in various diseases. In many cases, these cannot be separated and characterizations of their sizes conformations are difficult. We develop a single-molecule fluorescence method that can probe individual without separation determine the equilibrium constants oligomerization kinetics. By combining two- three-color FRET spectroscopy with lifetime analysis, it is possible to flexibility unambiguously....

In single-molecule Förster resonance energy transfer (FRET) spectroscopy, the dynamics of molecular processes are usually determined by analyzing fluorescence intensity donor and acceptor dyes. Since FRET efficiency is related to lifetimes, additional information can be extracted lifetime together. For fast where individual states not well separated in a trajectory, it easy obtain information. Here, we present analysis methods utilize from experiments, apply these three fast-folding,...

Abstract We describe theory, experiments, and analyses of three-color Förster resonance energy transfer (FRET) spectroscopy for probing sub-millisecond conformational dynamics protein folding binding disordered proteins. devise a scheme that uses single continuous-wave laser excitation the donor instead alternating one acceptors. This alleviates photophysical problems acceptors such as rapid photobleaching, which is crucial high time resolution experiments with elevated illumination...

Single-molecule free diffusion experiments enable accurate quantification of coexisting species or states. However, unequal brightness and diffusivity introduce a burst selection bias affect the interpretation experimental results. We address this issue with photon-by-photon maximum likelihood method, burstML, which explicitly considers criteria. BurstML accurately estimates parameters, including photon count rates, times, Förster resonance energy transfer (FRET) efficiencies, population,...

In single-molecule Förster resonance energy transfer (FRET) experiments, characterizing conformational dynamics from photon bursts emitted by diffusing molecules can be challenging due to the interplay of molecular transitions, translational diffusion, and background noise. This paper extends maximum likelihood analysis (burstML) incorporate both diffusion through laser spot, offering a comprehensive single molecules. The new approach integrates two previously developed methods: one...

Reversible diffusion-influenced pseudo first order reaction A+B ⇌C with static particles in excess is rigorously studied. Under most general assumptions, the problem of reversible kinetics reduced to consideration effective irreversible studied by conventional methods. In framework average t-matrix approximation (ATA) we reproduce some results derived earlier and establish their applicability limits. Rigorous investigation behavior at long times shows that t−3/2 law predicted reproduced ATA...

The probability distribution of observing N state-to-state transitions in a finite time t is calculated for an arbitrary kinetic scheme. In the Laplace domain, this can be expressed analytically terms (sI−K)−1 where K rate matrix. For long times simple expressions are found mean and variance number transitions.

Significance Repeated modification of a multisite protein plays key role in cell signaling. After an enzyme catalyzes reaction at one site, it can modify another site before diffusing away. This physical process, which is amplified the crowded environment cell, has been recently shown by stochastic simulations hundreds particles to dramatically change response biochemical network. Here we show that influence diffusion on be described much simpler way, introducing new connections into kinetic...