Separation of Fast and Slow Processes from a Stochastic Cage Model of Molecular Dynamics

The physical basis of model-free analysis of NMR relaxation data from proteins and complex fluids

NMR relaxation experiments have provided a wealth of information about molecular motions in macromolecules and ordered fluids. Even though a rigorous theory of spin relaxation is available, the complexity of the investigated systems often makes the interpretation of limited datasets challenging and ambiguous. To allow physically meaningful information to be extracted from the data without commitment to detailed dynamical models, several versions of a model-free (MF) approach to data analysis have been developed. During the past 2 decades, the MF approach has been used in the vast majority of all NMR relaxation studies of internal motions in proteins and other macromolecules, and it has also played an important role in studies of colloidal systems. Although the MF approach has been almost universally adopted, substantial disagreement remains about its physical foundations and range of validity. It is our aim here to clarify these issues. To this end, we first present rigorous derivations of the three well-known MF formulas for the time correlation function relevant for isotropic solutions. These derivations are more general than the original ones, thereby substantially extending the range of validity of the MF approach. We point out several common misconceptions and explain the physical significance of the approximations involved. In particular, we discuss symmetry requirements and the dynamical decoupling approximation that plays a key role in the MF approach. We also derive a new MF formula, applicable to anisotropic fluids and solids, including microcrystalline protein samples. The so-called slowly relaxing local structure (SRLS) model has been advanced as an alternative to the MF approach that does not require dynamical decoupling of internal and global motions. To resolve the existing controversy about the relative merits of the SRLS model and the MF approach, we formulate and solve a planar version of the SRLS model. The analytical solution of this model reveals the unphysical consequences of the symmetrical two-body Smoluchowski equation as applied to protein dynamics, thus refuting the widely held belief that the SRLS model is more accurate than the MF approach. The different results obtained by analyzing data with these two approaches therefore do not indicate the importance of dynamical coupling between internal and global motions. Finally, we explore the two principal mechanisms of dynamical coupling in proteins: torque-mediated and friction-mediated coupling. We argue by way of specific analytically solvable models that torque-mediated coupling (which the SRLS model attempts to capture) is unimportant because the relatively slow internal motions that might couple to the global motion tend to be intermittent (jumplike) in character, whereas friction-mediated coupling (which neither the SRLS model nor the MF approach incorporates) may be important for proteins with unstructured parts or flexibly connected domains.

Nonlocal electronic distribution in metallic clusters: a critical examination of aromatic stabilization

All-metal clusters, such as Al(4)M(4) (M = alkali metal ion), exhibit interesting features of multi-fold aromaticity/antiaromaticity. Such characteristics arise particularly because of the poor sigma-pi separation in this class of systems. This Account presents computational strategies to unambiguously determine the aromaticity/antiaromaticity characteristics of such clusters. Computations of the linear and nonlinear optical responses show that all-metal clusters are orders of magnitude more polarized than the conventional pi-conjugated molecules. We also propose new strategies to stabilize all-metal antiaromatic systems through complexation to transition metals and discuss mechanisms for substitution reactions within the conventional organometallic systems by Al(4)M(4). Additionally, we find that these all-metal clusters form stacked superclusters that are extremely stable and aromatic.

Molecular reorientation in hydrogen-bonding liquids: Through algebraic ∼t−3∕2 relaxation toward exponential decay

We present a model for the description of orientational relaxation in hydrogen-bonding liquids. The model contains two relaxation parameters which regulate the intensity and efficiency of dissipation, as well as the memory function which is responsible for the short-time relaxation effects. It is shown that the librational portion of the orientational relaxation is described by an algebraic approximately t(-32) contribution, on top of which more rapid and nonmonotonous decays caused by the memory effects are superimposed. The long-time behavior of the orientational relaxation is exponential, although nondiffusional. It is governed by the rotational energy relaxation. We apply the model to interpret recent molecular dynamic simulations and polarization pump-probe experiments on HOD in liquid D(2)O [C. J. Fecko et al., J. Chem. Phys. 122, 054506 (2005)].

Toward an integrated computational approach to CW-ESR spectra of free radicals

Interpretation of structural properties and dynamic behaviour of molecules in solution is of fundamental importance to understand their stability, chemical reactivity and catalytic action. Information can be gained, in principle, by a variety of spectroscopic techniques, magnetic as well as optical. In particular, continuous wave electron spin resonance (CW-ESR) measurements are highly informative. However, the wealth of structural and dynamic information which can be extracted from ESR spectroscopy is, at present, limited by the necessity of employing computationally efficient models, which are increasingly complex as they need to take into account diverse relaxation processes affecting the spectrum. In this paper, we address the basic theoretical tools needed to predict, essentially ab initio, CW-ESR spectra observables according to the stochastic Liouville equation (SLE) approach, combined with quantum mechanical and hybrid methods for the accurate and efficient computation of structural, spectroscopic and magnetic properties of molecular systems. We shall discuss, on one hand, the quantum mechanical calculation of magnetic observables, via density functional theory (DFT), time-dependent DFT (TD-DFT) and application of the polarizable continuum model (PCM) for the description of environmental effects, including anisotropic environments and systems where different regions are characterized by different dielectric constants. One the other hand, the explicit evaluation of dynamical effects will be discussed based on the numerically exact treatment of the SLE in the presence of several relaxation processes, which has been proven to be a challenging task.