Multiscale modeling for interpreting nuclear magnetic resonance relaxation in flexible molecules

Abstract

In this tutorial review, we provide a comprehensive description of a multiscale methodology tailored to the calculation of nuclear magnetic resonance (NMR) relaxation data of flexible molecules, based on the definition, parametrization, and solution of a Smoluchowski equation defined for a set of relevant molecular coordinates. While the method is applicable in principle to any collection of internal degrees of freedom, here we focus on flexibility described in terms of torsion angles under the paradigm of what we call the diffusive chain model. The theoretical basis of the multiscale stochastic approach to NMR spectroscopy is provided in detail. Computational aspects are discussed, pointing at a suggested set of specific software packages. To give to this contribution a hands-on component, a self-contained tutorial is made available as Supporting Information with the discussion of some examples taken from recently published studies.diffusive chain model, integrated computational approach, nuclear magnetic resonance, stochastic methods | I N T R O D U C T I O NIn this contribution, we present a general overview of a multiscale modeling approach to the interpretation of spectroscopic observables that are highly sensitive to molecular flexibility. In particular, we discuss a stochastic approach for the calculation of nuclear magnetic resonance (NMR) relaxation data of flexible molecules. In a multiscale spirit, all parameters entering the basic stochastic equation are calculated (or evaluated) using a proper level of description of the molecule, which can be quantum mechanical (QM), classical, or hybrid quantumclassical, depending on the type of the required parameter. After a short general review of the connection between molecular dynamics (MD) and spectroscopic observables, the discussion will be focused on NMR studies of molecules in solution, where the fast motional regime can be invoked.Our target is the description of the structural dynamics of a given flexible molecular system. MD is a fundamental ingredient, together with structural properties, that needs to be taken into account when interpreting, understanding, and predicting both single-molecule and bulk properties of matter. Just to mention a few important examples, dynamics affects proteins properties in a number of different ways, from tuning the binding properties of folded proteins to regulating pathways of folding and binding, from modulating allosteric regulation to controlling function in disordered/unstructured proteins or domains. [1,2] MD is also at the basis of function of molecular machines [3] and it can modulate charge transfer in molecular electronic devices. [4] Having access to molecular motions is, thus, of primary importance and a number of experimental (spectroscopic) techniques are at present available, which are split in two main branches: bulk and single-molecule experiments.NMR is the selected bulk technique to be described in this tutorial review. It is widely used in studying structure and dynamics of biomolecules, es...

DiTe2: Calculating the diffusion tensor for flexible molecules

“…However, the diffusion/friction tensor (together with the potential of mean force acting on the chosen collective coordinates) represents the key ingredient to access long time molecular dynamics and experimental techniques sensitive to slow coordinates, such as magnetic spectroscopy. Stochastic modeling of the chosen relevant degrees of freedom can be used, for example, to interpret molecular dynamics of flexible molecules from nuclear magnetic relaxation data . The new ability of DiTe2 to work with collective coordinates opens a route to connect experiments and molecular modeling of complex molecular systems in an ab initio fashion (i.e.…”

“…Stochastic modeling of the chosen relevant degrees of freedom can be used, for example, to interpret molecular dynamics of flexible molecules from nuclear magnetic relaxation data. [36] The new ability of DiTe2 to work with collective coordinates opens a route to connect experiments and molecular modeling of complex molecular systems in an ab initio fashion (i.e. without adjustable parameters).…”

Multiscale modeling of reaction rates: application to archetypal SN2 nucleophilic substitutions

“…In particular, several multiscale approaches have been presented for the study of flexible molecules in the literature. [4][5][6] In this work, we propose a multiscale computational protocol for evaluating the kinetic rate of an elementary chemical reaction, based on the well-established Kramers 7 description of reactive rare events and coupled with an accurate estimate of the generalized friction tensor of flexible molecules. A number of simple methods have been developed in the last hundred years to estimate the exponential pre-factor of the Arrhenius equation, trying to model equilibrium, non equilibrium, and even quantum systems.…”

Differential Dynamics at Glycosidic Linkages of an Oligosaccharide as Revealed by 13C NMR Spin Relaxation and Stochastic Modeling

“…Recently, we showed that excellent NMR spin relaxation data were possible to obtain for a single site-selectively 13 C-labeled disaccharide, where the relaxation parameters were possible to model in very good agreement (average error <2%) using a stochastic approach. In particular, we employed the diffusive chain model (DCM), which proved very effective to predict NMR relaxation data of “linear” oligosaccharides, with two, three, and five sugar units. − The method is based on the description of the internal degrees of freedom (dof) of a molecule in terms of bonds, bond angles, and dihedral angles. The former two types of internal dof are considered fast and, therefore, not relevant to NMR-based investigations of molecular structure and dynamics.…”