Illuminating the mechanistic roles of enzyme conformational dynamics.

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.

Detection of intensity change points in time-resolved single-molecule measurements.

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.

Quantitative single-molecule conformational distributions: a case study with poly-(L-proline).

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.

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.

Biindanylidenes: role of central bond torsion in nonvertical triplet excitation transfer to the stilbenes.

The stilbenes were proposed to function as nonvertical triplet excitation (NVET) acceptors for energy-deficient donors because rotation about the central bond diminishes the energy gap between ground and triplet energy surfaces. Recently, the role of central bond torsion in facilitating NVET to cis-stilbene (c-St) was questioned because the behavior of 2,3-diphenylnorbornene as a triplet energy acceptor is similar to that of cis-stilbene. On the basis of the assumption that the rigidity of the norbornene skeleton precludes torsional displacement of the phenyl rings in the triplet state, an alternative mechanism was proposed involving phenyl-vinyl torsion as the key reaction coordinate for NVET to c-St. However, this proposal is inconsistent with theory, which predicts that the triplet state energy minimum corresponds to a geometry with significant displacement of the phenyl rings of 2,3-diphenylnorbornene from a common plane. We now provide experimental evidence demonstrating that central bond torsion is the key coordinate for NVET to stilbenes. Comparison of the activation parameters for the two rigid stilbene analogues, cis- and trans-1,1'-biindanylidene (c-Bi and t-Bi) to those for the stilbenes, shows that the excitation transfer processes remain nonvertical despite the strong structural inhibition of phenyl-vinyl torsion; the relatively small preexponential factors of the respective isomers are almost identical. Their magnitude is a measure of the attenuation introduced by Franck-Condon overlap factors which decrease as the torsional state quantum number corresponding to the transition state increases. These results and results from theoretical calculations are consistent with central bond torsion as the key reaction coordinate in NVET to the biindanylidenes and the stilbenes. The crystal structure of t-Bi shows it to be strictly planar, eliminating phenyl-vinyl torsion toward planarity as a crucial NVET reaction coordinate.