An approach to find transition pathways in complex systems is presented. The method, which is related to the string method in collective variables of Maragliano et al. (J. Chem. Phys. 2006, 125, 024106), is conceptually simple and straightforward to implement. It consists of refining a putative transition path in the multidimensional space supported by a set of collective variables using the average dynamic drift of those variables. This drift is estimated on-the-fly via swarms of short unbiased trajectories started at different points along the path. Successive iterations of this algorithm, which can be naturally distributed over many computer nodes with negligible interprocessor communication, refine an initial trial path toward the most probable transition path (MPTP) between two stable basins. The method is first tested by determining the pathway for the C7eq to C7ax transition in an all-atom model of the alanine dipeptide in vacuum, which has been studied previously with the string method in collective variables. A transition path is found with a committor distribution peaked at 1/2 near the free energy maximum, in accord with previous results. Last, the method is applied to the allosteric conformational change in the nitrogen regulatory protein C (NtrC), represented here with a two-state elastic network model. Even though more than 550 collective variables are used to describe the conformational change, the path converges rapidly. Again, the committor distribution is found to be peaked around 1/2 near the free energy maximum between the two stable states, confirming that a genuine transition state has been localized in this complex multidimensional system.

The nitroxide spin label 1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl-methanethiosulfonate (MTSSL), commonly used in site-directed spin labeling of proteins, is studied with molecular dynamics (MD) simulations. After developing force field parameters for the nitroxide moiety and the spin label linker, we simulate MTSSL attached to a polyalanine alpha-helix in explicit solvent to elucidate the factors affecting its conformational dynamics. Electron spin resonance spectra at 9 and 250 GHz are simulated in the time domain using the MD trajectories and including global rotational diffusion appropriate for the tumbling of T4 Lysozyme in solution. Analysis of the MD simulations reveals the presence of significant hydrophobic interactions of the spin label with the alanine side chains.

Multifrequency electron spin resonance (ESR) spectra provide a wealth of structural and dynamic information about the local environment of the spin label, and indirectly, about the protein to which they are attached. Relating the features of the observed spectra to the underlying molecular motions and interactions is, however, challenging. To make progress toward a rigorous interpretation of ESR spectra, we perform extensive molecular dynamics (MD) simulations of fully solvated T4 Lysozyme, labeled with the spin label MTSSL at positions 72 and 131. These two sites have been the object of numerous experimental studies, and are generally considered as prototypical solvent-exposed sites on the surfaces of α-helices. To extend the time window afforded by the MD simulations, stochastic Markov models reflecting the dynamics of the spin label side chains in terms of their rotameric states are constructed from the trajectories. The calculated multifrequency ESR spectra are in very good agreement with experiment for three different magnetic field strengths without adjusting any parameters. During the trajectories, the spin labels interconvert among a fairly large number of conformations, and display a propensity to form interactions with protein residues other than their nearest neighbors along the helix. The detailed picture of the spin label emerging from the MD simulations provides useful insight into the molecular origins of the available spectroscopic and crystallographic data.

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.

The magnetic resonance signal obtained from nuclear spins is strongly affected by the presence of nearby electronic spins. This effect finds application in biomedical imaging and structural characterization of large biomolecules. In many of these applications nitroxide free radicals are widely used due to their non-toxicity and versatility as site-specific spin labels. We perform molecular dynamics simulations to study the electron-nucleus interaction of the nitroxide radical TEMPOL and water in atomistic detail. Correlation functions corresponding to the dipolar and scalar spin-spin couplings are computed from the simulations. The dynamic nuclear polarization coupling factors deduced from these correlation functions are in good agreement with experiment over a broad range of magnetic field strengths. The present approach can be applied to study solute-solvent interactions in general, and to characterize solvent dynamics on the surfaces of proteins or other spin-labeled biomolecules in particular.

Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of ns) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, twostep procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin labeled poly-alanine alpha helix in explicit solvent.

Dynamic nuclear polarization (DNP) at high magnetic fields (9.2 T, 400 MHz (1)H NMR frequency) requires high microwave power sources to achieve saturation of the EPR transitions. Here we describe the first high-field liquid-state DNP results using a high-power gyrotron microwave source (20 W at 260 GHz). A DNP enhancement of -29 on water protons was obtained for an aqueous solution of Fremy's Salt; in comparison the previous highest value was -10 using a solid-state microwave power source (maximum power 45 mW). The increased enhancements are partly due to larger microwave saturation and elevated sample temperature. These experimentally observed DNP enhancements, which by far exceed the predicted values extrapolated from low-field DNP experiments, demonstrate experimentally that DNP is possible in the liquid state also at high magnetic fields.

Pulsed electron double resonance (PELDOR) spectroscopy reveals a prearranged tertiary structure of the 27 nucleotides long engineered neomycin-responsive riboswitch. Measured distances between spin labels at positions U4-U14, U4-U15, U14-U26, and U15-U26 were unchanged upon neomycin binding which implies that the global stem-loop architecture is preserved in the absence and presence of the ligand. On the basis of our results, we infer that low-temperature PELDOR data unambiguously demonstrate the existence of an enthalpically favorable set of RNA conformations ready to bind the ligand without major global rearrangement.