The measurement of anisotropic spin interactions, such as residual dipolar couplings, in partially ordered solutions can provide valuable information on biomolecular structure. While the information can be used to refine local structure, it can make a unique contribution in determining the relative orientation of remote parts of molecules, which are locally well structured, but poorly connected based on NOE data. Analysis of dipolar couplings in terms of Saupe order matrices provides a concise description of both orientation and motional properties of locally structured fragments in these cases. This paper demonstrates that by using singular value decomposition as a method for calculating the order matrices, principal frames and order parameters can be determined efficiently, even when a very limited set of experimental data is available. Analysis of 1H-15N dipolar couplings, measured in a two-domain fragment of the barley lectin protein, is used to illustrate the computational method.

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.

The measurement of fluorescence from single protein molecules has become an important new tool in the study of dynamic processes, allowing for the direct visualization of the motions experienced by individual proteins and macromolecular complexes. The data from such single-molecule experiments are in the form of photon trajectories, consisting of arrival times and wavelength information on individual photons. The analysis of photon trajectories can be difficult, particularly if the motions are occurring at rates comparable to the photon arrival rate or in the presence of noise. In this paper, we introduce the use of hidden Markov models (HMMs) for the analysis of photon trajectory data that operate using the photon data directly, without the need for ensemble averaging of the data as implied by correlation function analysis. Using a simple kinetic model, we examine the relationship between the uncertainty in the estimates of the motional rate and the photon detection rate. Remarkably, we obtain relative uncertainties in the rate constants of as little as 3% even when the interconversion rate is equal to the photon detection rate, and the uncertainty increases to only 10% when the interconversion rate is 10 times the photon detection rate. This suggests that useful information can be obtained for much faster kinetic regimes than have typically been studied. We also examine the impact of background photons on the determination of the rate and demonstrate that the HMM-based approach is robust, displaying small uncertainties for background photon arrival rates approaching that of the signal. These results not only are relevant in establishing the theoretical limits on precision, but are also useful in the context of experimental design. Finally, to demonstrate how the methodology can be extended to more complex kinetic models and how it can allow one to make use of the full power of statistics for purposes of model evaluation and selection, we consider a four-state kinetic model for protein conformational transitions previously studied by Schenter et al. (J. Phys. Chem. A1999, 103, 10477). We show how an HMM can be used as an alternative to higher-order correlation function analysis for the detection of "conformational memory" and apparent non-Markovian dynamics arising from such temporally inhomogeneous kinetic schemes.

We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large (Ϸ10 6 ) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the ␣-helix͞ ␤-hairpin interconversion.graph ͉ master equation ͉ protein G P rotein folding is a fundamental problem in modern structural biology, and recent advances in experimental techniques have helped to elucidate some of the thermodynamic and kinetic features that underlie different stages of the folding process (1-3). Computer simulations using reduced (4-11) and atomistic molecular models (12-21) have played a central role in the interpretation of experimental studies. Although reduced models have provided considerable insight into the overall mechanisms of protein folding, especially in helping to clarify the nature of folding funnels, intermediates, and kinetic bottlenecks, they are limited in their ability to explore the detailed molecular aspects of folding. However, because of the large number of degrees of freedom and the rarity of folding events even in small model systems, all-atom simulations require both considerable computational resources and ingenuity to obtain meaningful results; a variety of methods have been developed to increase simulation efficiency.A particularly powerful technique for the calculation of free energy surfaces and other thermodynamic properties of complex systems is replica exchange molecular dynamics (REMD) (22), in which a generalized ensemble of the system is simulated in parallel over a range of temperatures. Periodically, coordinates are exchanged by using a Metropolis criterion that ensures that at any given temperature a canonical distribution is realized and allows for more efficient barrier crossing than could be obtained with conventional simulation methods. Although REMD is a powerful method for exploring free energy landscapes, it does not provide direct information about kinetics. To study folding by using all-atom effective potentials, heterogeneous distributed computing (16,19) and transition path sampling (23, 24) techniques have been used. Although the former can enhance sampling by combining information from a large number of short MD trajectories ''steered'' by rare events, these techniques can introduce a bias toward fast events in the ensemble average of the reactive trajectories (25). Transition path sampling (23,24) can yield quantitative estimat...