We present a method for the analysis of optical single molecule emission data that exhibit discrete intensity jumps. This new method uses a generalized likelihood ratio test that determines the location of an intensity change point based on individual photon arrival times. This test is applied recursively to an entire single molecule intensity trajectory, thus finding each change points. Expectation-maximization clustering and the Bayesian information criterion is then used for accurate determination of the true number of states accessible to the system. This procedure allows rigorous and quantitative determination of intensity change points without the artificial time resolution limitations that arise from binning and thresholding.

Many enzymes mold their structures to enclose substrates in their active sites such that conformational remodeling may be required during each catalytic cycle. In adenylate kinase (AK), this involves a large-amplitude rearrangement of the enzyme's lid domain. Using our method of high-resolution single-molecule FRET, we directly followed AK's domain movements on its catalytic time scale. To quantitatively measure the enzyme's entire conformational distribution, we have applied maximum entropy-based methods to remove photon-counting noise from single-molecule data. This analysis shows unambiguously that AK is capable of dynamically sampling two distinct states, which correlate well with those observed by x-ray crystallography. Unexpectedly, the equilibrium favors the closed, active-site-forming configurations even in the absence of substrates. Our experiments further showed that interaction with substrates, rather than locking the enzyme into a compact state, restricts the spatial extent of conformational fluctuations and shifts the enzyme's conformational equilibrium toward the closed form by increasing the closing rate of the lid. Integrating these microscopic dynamics into macroscopic kinetics allows us to model lid opening-coupled product release as the enzyme's rate-limiting step.conformational equilibrium ͉ rate-limiting step ͉ single-molecule FRET ͉ adenylate kinase P roteins such as enzymes are flexible with a range of motions spanning from picoseconds for localized vibrations to seconds for concerted global conformational rearrangements (1). Despite their randomly fluctuating environment, in which stochastic collisions with solvent molecules drive changes in tertiary structure, enzymes have evolved to catalyze reactions efficiently and specifically. Indeed, conformational transitions have been postulated to play a central role in enzyme functions in a wide variety of ways, including direct contribution to catalysis (2), allosteric regulation (3), and large-scale conformational changes in response to ligand binding (4). Most of our current understanding of structural motions in solution comes from NMR experiments (5) as well as from molecular dynamics simulations (6), approaches that are best suited to study dynamics in the picoto millisecond time scales. Because catalysis in enzymes frequently occurs in the submillisecond to minute time regime, our current understanding of the relationship between enzyme function and conformational dynamics comes from NMR experiments involving relatively localized motions of active site forming loops on the submillisecond time scale (7-10). However, many enzymes contain active sites located in between domains in which large-amplitude, low-frequency domain motions are required to complete their Michaelis-Menten enzyme-substrate complexes. Even simple questions regarding these transitions remain generally unanswered: What is the number and range of conformational states accessible to enzymes during their catalytic cycle? How does the enzyme's conformation respond to interac...

Precise measurement of the potential of mean force is necessary for a fundamental understanding of the dynamics and chemical reactivity of a biological macromolecule. The unique advantage provided by the recently developed constant-information approach to analyzing time-dependent single-molecule fluorescence measurements was used with maximum entropy deconvolution to create a procedure for the accurate determination of molecular conformational distributions, and analytical expressions for the errors in these distributions were derived. This new method was applied to a derivatized poly(L-proline) series, P(n)CG3K(biotin) (n = 8, 12, 15, 18, and 24), using a modular, server-based single-molecule spectrometer that is capable of registering photon arrival times with a continuous-wave excitation source. To account for potential influence from the microscopic environment, factors that were calibrated and corrected molecule by molecule include background, cross-talk, and detection efficiency. For each single poly(L-proline) molecule, sharply peaked Förster type resonance energy transfer (FRET) efficiency and distance distributions were recovered, indicating a static end-to-end distance on the time scale of measurement. The experimental distances were compared with models of varying rigidity. The results suggest that the 23 angstroms persistence length wormlike chain model derived from experiments with high molecular weight poly(L-proline) is applicable to short chains as well.

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.

Quantum yields for the interconversion of the all- cis,trans,cis,3, in methylcyclohexane (MCH) or acetonitrile (AN) following 366 nm excitation show these processes to be relatively inefficient. Their dependence on the concentration of the DPH reveals significant participation of triplet states in the overall process. Despite very low intersystem crossing quantum yields (0.029 and 0.010 in MCH and AN, respectively) singlet and triplet contributions in the photoisomerization of all-trans-1,6-diphenyl-1,3,5-hexatriene are roughly equal in MCH, and, for the trans,cis,trans isomer, in AN. However, in AN the cis,trans,trans isomer forms nearly exclusively by a singlet pathway from the other two isomers. The cis,cis,trans isomer, a very minor component in photostationary states, appears to form primarily from the cis,trans,trans isomer whose excited singlet state also gives another isomer, tentatively identified as ctc-DPH. The major radiationless channel of the excited singlet state of each DPH isomer is direct decay to the original ground state. Barriers to torsional relaxation of the planar lowest DPH excited singlet states (2 1 A g and 1 1 B u ) must be significantly higher than previously supposed. Photoisomerization quantum yields of all-trans-DPH in the presence of fumaronitrile (FN) are also separated into singlet and triplet contributions. Fumaronitrile quenches DPH fluorescence and singlet contributions to the photoisomerization equally, but enhances DPH triplet formation and the triplet contribution to the photoisomerization. Radical cations of DPH form in AN but do not participate in isomer interconversion.