Analyzing complicated protein folding kinetics rapidly by analytical Laplace inversion using a Tikhonov regularization variant

Implementation and evaluation of data analysis strategies for time-resolved optical spectroscopy

Time-resolved optical spectroscopy plays a key role in illuminating the mechanisms of many fundamental processes in physics, chemistry, and biology. However, to extract the essential information from the highly complex time-resolved data, advanced data analysis techniques are required. Here we present the implementation strategies and the evaluation of the familiar global lifetime and target analysis as well as the not so widely adopted lifetime distribution analysis (LDA). Furthermore, we demonstrate the implementation of analysis strategies dealing with a number of artifacts inherently present in data from ultrafast optical experiments. The focus of the work is placed on LDA as it allows invaluable exploration depth of the kinetic information contained in the experimental data. We establish a clear regularization procedure for the use of LDA in ultrafast optical spectroscopy and evaluate the performance of a number of factors that play a role in the reliable reconstruction of lifetime distributions. Our results show that the optimal regularization factor can be determined well with the L-curve and the generalized cross-validation techniques. Moreover, the performance evaluations indicate that the most efficient regularization norm is the identity matrix. The analytical procedures described in this work can be readily implemented and used for the analysis of any time-resolved data.

Photo-physical properties of 2-(1-ethynylpyrene)-adenosine: influence of hydrogen bonding on excited state properties

The photo-physical properties of 2-(1-ethynylpyrene)-adenosine (PyA), a fluorescent probe for RNA dynamics, were examined by solvation studies. The excited-state dynamics display the influence of the vicinity on the spectral features. Combining improved transient absorption and streak camera measurements along with a new analysis method provide a detailed molecular picture of the photophysics. After intramolecular vibrational energy redistribution (IVR), two distinct states are observed. Solvent class (protic/aprotic) and permittivity strongly affect the properties of these states and their population ratio. As a result their emission spectrum is altered, while the fluorescence quantum yield and the overall lifetime remain nearly unchanged. Consequently, the hitherto existing model of the photophysics is herein refined and extended. The findings can serve as basis for improving the information content of measurements with PyA as a label in RNA.

Filtering artifacts from lifetime distributions when maximizing entropy using a bootstrapped model

The maximum entropy method (MEM) has been used in many studies to reliably recover effective lifetimes from kinetics, whether measured experimentally or simulated computationally. Here, recent claims made by Mulligan et al. regarding MEM analyses of kinetics (Anal. Biochem. 421 (2012) 181-190) are shown to be unfounded. Their assertion that their software allows "analysis of datasets too noisy to process by existing iterative search algorithms" is refuted with a MEM analysis of their triexponential test case with increased noise. In addition, it is shown that lifetime distributions recovered from noisy kinetics data with the MEM can be improved by using a simple filter when bootstrapping the prior model. When deriving the bootstrapped model from the lifetime distribution obtained using a uniform model, only the slower processes are represented as Gaussians in the bootstrapped model. Using this new approach, results are clearly superior to those of Mulligan et al. despite the presence of increased noise. In a second example, ambiguity in the interpretation of Poisson kinetics in the presence of scattered excitation light is resolved by filtering the prior model.

Slow unfolded-state structuring in Acyl-CoA binding protein folding revealed by simulation and experiment

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ~10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (~100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.