Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

Abstract

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a "chevron" shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.

Protein folding transition path times from single molecule FRET

“…Szabo and Gopich have developed a very powerful maximum likelihood method for analyzing such photon trajectories [21,61,62]. The analysis with their method is considerably simplified if a model has already been firmly established in ensemble measurements.…”

Pitching Single-Focus Confocal Data Analysis One Photon at a Time with Bayesian Nonparametrics

“…Indeed, existing methods make assumptions that render them inapplicable to diffusion through inhomogeneously illuminated volumes. For example, they assume uniform illumination [24,29], apply downsampling or binning and thereby reduce temporal resolution to exploit existing mathematical frameworks such as the hidden Markov model [22,25,28,81,82], or focus on immobile molecules [25,[32][33][34]. More recently, fluorescence-based nanosecond FCS approaches, in which the data are still correlated under the assumption that the time trace reports on processes at equilibrium, have been used to obtain information on rapid fluctuations in proteins [35].…”

“…Previously proposed methods to analyze single-photon measurements [22][23][24][25][26][27][28][29][30] make assumptions that render them inappropriate for imaging molecules moving through inhomogeneously illuminated volumes [24]. For example, for the analysis of single molecule fluorescence resonance energy transfer (FRET), existing methods assume that the photon interarrival times reflect only biomolecular conformational transitions [24,25,31] but not diffusive motion of the entire biomolecule [25,[32][33][34], and so are appropriate only for experiments on immobilized molecules. Along the same lines, existing methods combine FRET with FCS [35] to quantify nanosecond dynamics; however, they do not directly exploit single-photon measurements.…”

AimR Adopts Preexisting Dimer Conformations for Specific Target Recognition in Lysis-Lysogeny Decisions of Bacillus Phage phi3T

“…With all three fluorescence time traces recorded, the signals from the donor-only or acceptor-only protein molecules were filtered out, so as to ensure that an f Dex/Aem photon only arises from a doubly labeled protein. A burst search was performed using a start/stop criterion as described [ 29 , 30 ].…”